Phet simulations electric field hockey

Physic Lab Work

Electricity and Magnetism Simulation Worksheets and Labs

Physics 152 Online, CSU Long Beach

Dr. Thomas Gredig

Copyright c© 2016 Thomas Gredig ALL RIGHTS RESERVED. PUBLISHED BY THOMAS GREDIG

THOMASGREDIG.COM

ALL RIGHTS RESERVED. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without explicit written permission from the publisher. Edition, June 2016

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1 Activity Worksheets 8

1.2 Hands-on Experiments 8

1.3 Team Work 10

2 Lab Report Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 Online Lab Organization 13

2.2 Report Structure 13

2.3 Report Submission 15

2.4 Grading Rubric 15

2.5 Measuring Data 15

2.6 Ethics 16

2.7 Experiments 16

2.8 Arduino 16

2.9 Fitting Data 17

3 Practice Exams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1 Problem with Solution 21

3.2 Midterm Practice Problems 22

3.3 Final Exam Practice Problems 23

3.4 Basic Relations in Electricity and Magnetism 24

3.5 Reference 26

I Interactive Simulations

4 Activity 14: Electric Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.1 Objective 33

4.2 Background 33

4.3 Prediction: Charge Configurations 34

4.4 Calculation 35

4.5 PHeT Simulation 35

5 Activity 15: Electric Field Hockey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.1 Prediction 37

5.2 PhET simulation 39

5.3 Evaluation 39

6 Activity 16: Electric Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6.1 Prediction 41

6.2 Simulation 42

6.3 Evaluation 42

7 Activity 17: Electric Field from Irregular Shape . . . . . . . . . . . . . . . . . . 43 7.1 Background 43

7.2 Prediction 43

7.3 Calculation 44

7.4 Evaluation 44

8 Activity 18: Light Bulbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 8.1 Prediction 47

8.2 Mesaurements 49

8.3 Evaluation 50

9 Activity 19: RC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 9.1 Background 53

9.2 Predictions 53

9.3 Measurements 54

9.4 PhET Simulation 56

10 Activity 20: Series and Parallel Resistors . . . . . . . . . . . . . . . . . . . . . . . . 59 10.1 Series Circuit in a Parallel Circuit 59

10.2 Parallel Circuit in a Series Circuit 60

10.3 Series Circuit in a Parallel Circuit in a Series Circuit 60

11 Activity 22: Faraday’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 11.1 Background 63 11.2 Bar Magnet 63 11.3 Electromagnet 65 11.4 Pickup Coil 65 11.5 Transformer 66 11.6 Generator 67

12 Activity 23: Radio Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 12.1 Prediction 69 12.2 Simulation 69

II Hands-on Experiments

13 Lab 1: Measuring Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 13.1 Tools 75 13.2 Prediction 75 13.3 Experiment 76 13.4 Evaluation 76

14 Lab 2: Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 14.1 Tools 77 14.2 Prediction 77 14.3 Experiment 78 14.4 Evaluation 78

15 Lab 3: Arduino Battery Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 15.1 Tools 79 15.2 Prediction 79 15.3 Experiment 80 15.4 Evaluation 81

16 Lab 4: Resistor Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 16.1 Tools 83 16.2 Prediction 83 16.3 Experiment 84 16.4 Evaluation 84

17 Lab 5: Voltage Divider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 17.1 Tools 85 17.2 Prediction 85 17.3 Experiment 85

17.4 Evaluation 86

18 Lab 6: RC circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 18.1 Tools 87 18.2 Prediction 87 18.3 Experiment 88 18.4 Evaluation 88

III Team Tasks

19 Team Task 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 19.1 Relevant Chapter 93 19.2 Electron mass 93

20 Team Task 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 20.1 Midterm Preparation 95

21 Team Task 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 21.1 Electric Field of Any Shape 97

22 Team Task 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 22.1 Resistor Network 101

23 Team Task 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 23.1 Problem Solving 103

24 Team Task 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 24.1 Reflections 105

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

1. Introduction

UNDOUBTEDLY experiments provide an real value to any learning experience as a way ofconnecting the real-world with the abstract. This is particularly true for the topic of "Electricity and Magnetism", which deals with quantities that are very real, electric and magnetic fields, but our senses are poor at measuring (although for electromagnetic waves in the visible range, our eyes help).

Experiments, however, can be complex to setup and costly. An intermediate experience, therefore, are interactive simulations. These are computer programs that have programmed algorithms, which simulate certain settings. Many simulations are available nowadays, but I would like to point out a particular project, which was sponsored by the National Science Foundation, and developed by the University of Colorado, it is called the PhET simulations, available at https: //phet.colorado.edu/. A collection of interactive simulations for the Sciences and Mathematics made available to the public through federal science grants. We provide you with a set of worksheets that guide you using these simulations in part I starting on page 33.

In addition to the simulations, the online PHYS 152 lab includes hands-on experiments detailed in part II starting on page 75. The procedure for these labs is detailed in Chapter 2 starting on page 13. It is based on a home experimental kit and so all experiments can be performed with the help of this kit, a smartphone, computer, and everyday tools. Indeed, the aim of this series of small experiments related to discovering electricity and magnetism is to make the procedures applicable, so that you can carry out many more of the same type of experiments on your own. Therefore, this course provides only the beginning boundaries of much more exploration. A home kit is therefore ideal as it gives you some tools needed to continue this scientific process.

Lastly, science and engineering are highly collaborative disciplines with team tasks. Sharing, communicating, and evaluating each other is an everyday task of professionals in this field. A paradigm for this is research. It is based on proposals of experiments that are evaluated and vetted based on their merits and benefits. The best experiments are conducted, data is acquired and a lab report is submitted for publication. Peers review these reports before some are accepted for publication. You have the opportunity to practice and learn this process in small teams using an asynchronous discussion forum. The teams are small (around 5 participants) formed by the

https://phet.colorado.edu/
https://phet.colorado.edu/
8 Chapter 1. Introduction

instructor. The team will work on team tasks (see part III on page 93) using team roles that are mapped to the specific steps of problem solving.[4, 3] These roles are explained on page 10, with the underlying understanding that an expert wears all hats at the same time, but for a learner focusing on one role will be good practice. Additionally, we will use these teams to evaluate lab reports. The team will give feed-back based on the lab report grading rubric (page 15) to selected lab reports. This mechanism provides multiple benefits, for one you get to see how your peers write reports, normalizing your experience, applying the grading rubric focuses your attention to critical portions of the report, and finally you can received feed-back from teams to improve your reports. Lastly, this process mirrors the professional approach and eases a pathway into a career.

1.1 Activity Worksheets The following worksheets will provide you some guidance as how to use those simulations and others by asking questions. For the purpose of effective learning, it is important to first reflect on your current knowledge. This is generally done by making predictions, which is to think about different scenarios related to the topic and based on your knowledge foresee outcomes. You may be tempted to guess the answer without much reflection, or look up the solution.[5] Resist this temptation, as this step is crucial in memory building. It is important to write those predictions down. In the next step, you will use the simulations and recreate the questions, then make observations of the results. In the third step, you will compare the predictions with the observations and note any discrepancies. In the last step, you reflect on your findings and try to apply the learned experiences to other settings, which are similar. If done properly, this procedure is extremely efficient. Essentially, you know that learning would occur, if your predictions would be different in some way from your observations. Note that sometimes, seemingly the predictions agree with your observations, there are fine discrepancies, or nuances, that are different, scientists and engineers are good at detecting those details and ponder about them. During the course, different activities are assigned with specific deadlines. Submit your worksheets as single PDF files that you can easily scan with one of many available PDF scanners. From your phone, you can use CamScanners, GeniusScan, etc. there are other ways as well. You can either print the worksheets and directly work on them, using the space, or you can use separate sheets for your answers. Always make sure (to get full points) that you label all the questions in accordance to the numbering scheme from this worksheet. For every activity, you may also be asked to capture a screenshot of the simulation and include it. For full points, capture and submit a unique screenshot that shows that it is your work. It is also important to label the axes of all graphs and include units as well. Some examples are given in the worksheets.

1.2 Hands-on Experiments There are several experimental hands-on labs that can be carried out at home. The first step will be to clarify the experimental procedures and writing down the predictions. In your notebook, you write down the procedure of how you will carry out the experiment, the hypothesis, and the predictions. In the next step, you build the experiment and take data. Commonly, data needs to be taken several times in order to verify the experimental procedure and the reproducibility. The repetition also gives you a way to judge the reliability of the data and the error bars. During the experiment, all results are carefully noted in the lab notebook. At this point, you are ready to write the report according to the guidelines listed on page 13; scientists and engineers use this method and you can find many sample reports at https://arxiv.org/. We strive to learn from the experts. Note that the report provides both details about the experimental method used, the results, and analysis. It also includes photos of the experimental setup with the date in the photograph, see Fig. 2.2.1. A lab report has graphs, which you can generate with OpenCalc (https://www.openoffice.org/

https://arxiv.org/
https://www.openoffice.org/product/calc.html
https://www.openoffice.org/product/calc.html
1.2 Hands-on Experiments 9

product/calc.html), Google Sheets (https://www.google.com/sheets/about/), RStudio (https://www.rstudio.com/), R-Fiddle (http://www.r-fiddle.org/#/), gnuplot (http:// www.gnuplot.info/), or Plot2 for Mac (http://apps.micw.eu/apps/plot2/). All of these programs are free, and several open-source, most can be installed on different platforms. The lab report is, then, an independent, complete summary of the experiment you conducted.

Before reports are published, scientists and engineers, peer-review the reports and give feed-back. In the course, this process is called "lab evaluations", and you are responsible to review lab reports of your peers based on a rubric (see page 15). Reading your peer’s lab reports and evaluating them is a powerful learning tool that you should not underestimate. Not all reports will get published, based on the reviews and his or her judgement of the report, the editor (here, the instructor) will make the final evaluation of the report.

In order to make the experimental kit, or tool box, cost effective, we have adopted the micro- controller platform called Arduino. The Arduino controller is open-source and inexpensive (order of USD 10 – 20), widely available. There are many types of Arduino, for the course, the basic UNO type will be sufficient. The Arduino board comes with sensor inputs and also with outputs. We will use these sensors to connect resistor circuits, and test RC circuits. The board connects via USB port to a computer; details are provided on the website https://www.arduino.cc/ and the software is installed from the "Download" button.

1.2.1 Experimental Kit

You will need to purchase an experimental Arduino kit in order to perform the experiments. You have several options to purchase or build the kit. Reviewing the labs, you can see all the required tools and materials listed in part II starting on page II. Here is a summary:

• Arduino micro-controller with USB (http://tinyurl.com/phys152Arduino) • breadboard and wires • several resistors (1 kΩ, 10 kΩ, 1 MΩ) • one or more capacitors (0.5 µF or more, product of largest resistor multiplied with capacitance

should equal about 1 s) • basic compass (possibly compass of phone) • Al foil, drinking straws, other home materials

You can build your own kit based on the previous list, or you can purchase a package, which contains all of these items and a few more.

• Sunfounder Project Super Starter Kit for Arduino UNO R3 at tinyurl.com/phys152kit2 plus an Arduino Board at http://tinyurl.com/phys152Arduino

• Arduino UNO R3 Ultimate Starter Kit at tinyurl.com/phys152kit1 • KT003 Arduino UNO Start Kit with Bread Plate at http://tinyurl.com/phys152kit4

(does not include capacitor, see page 87)

Note that the Sunfounder Kit (tinyurl.com/phys152kit2) is probably the best and it includes 100 nF capacitors and one 5 MΩ resistor, which would give you a time constant of 0.5 s, a bit less than 1 s. However, if you put all 4 capacitors in parallel, you can quadruple the time constant by increasing the capacitance to 400 nF, which is quite sufficient.

You can also purchase capacitors and resistors separately from several stores and online from Mouser at http://www.mouser.com/, searching for multilayer "capacitors 10 uF", you will find that the cost is less than one US dollar.

https://www.openoffice.org/product/calc.html
https://www.openoffice.org/product/calc.html
https://www.google.com/sheets/about/
https://www.rstudio.com/
http://www.r-fiddle.org/#/
http://www.gnuplot.info/
http://www.gnuplot.info/
http://apps.micw.eu/apps/plot2/
https://www.arduino.cc/
http://tinyurl.com/phys152Arduino
tinyurl.com/phys152kit2
http://tinyurl.com/phys152Arduino
tinyurl.com/phys152kit1
http://tinyurl.com/phys152kit4
tinyurl.com/phys152kit2
http://www.mouser.com/
10 Chapter 1. Introduction

1.3 Team Work In addition to individual assignments, there are some problems for small teams. For the teams to work cooperatively, we have implemented some features that will help with the asynchronous online discussions. In particular, we have assigned roles, which help you train each step of the problem solving (see section 3 on page 21). Note that an expert problem solver will rotate independently through all roles (team leader, planner, researcher, executive, and skeptic). In order to become or improve as an expert problem solver, it is important to practice / train each specific step independently. The grading and point distribution of the midterm and final exam is based on the problem solving steps or the roles outlined here. Once you master each step, you can put them together and gradually become an expert yourself. If you are interested in more details and the physics education research, you can read more in this booklet: http://groups.physics.umn.edu/physed/Research/CGPS/GreenBook.html Use the team work assignments to your advantage, namely to make learning more productive.[1] Somewhat surprisingly, the benefits, although different in aspects, are to all learners regardless of their prior expertise.

1.3.1 Team Roles Here is a summary of the team roles. You will be assigned different roles in different tasks. As a member of your group you work holistically, but focus on your specific role. • Team Leader: motivates team, sends messages to the team, makes sure the team understands

the task, helps make major decisions, and keeps track of time, and posts the solution. The team leader of the team may also help assign sub tasks to the team and makes sure everyone stays motivated. The team leader is responsible to post a summary of the finding in the showcase. • Planner: restates the problem in his/her own words, draws a diagram including a coordinate

system, draws a sketch and identifies parameters useful in the problem. The planner typically identifies the important variables. Each sketch and diagram generally includes a coordinate system with labeled axes. • Researcher: identifies an underlying physical principle / concept useful to solve the problem,

such Coulomb’s Law, Mobile Charges in Conductor, . . . The researcher typically categorizes the problem (which section / chapter) and provides any definitions, or fundamental relations. • Executive: Applies the concept / principle to the specific problem outlined by the planner

and finds a concrete solution. The executive would apply the researchers definitions and fundamental relations to the specific problem and find a specific result. • Skeptic: Makes sure the planner, researcher, and executive are on the right track, by asking

questions, such as is this right? should we consider something else? did we assume anything here? then at the end, the skeptic says: are the units correct? did we answer all the questions? does the solution make sense? The skeptic provides critical feed-back to all members of the team.

1.3.2 Problem Solving Quantitative problem solving is a marketable skill. Any physics course is particularly geared towards training those skills. You are provided with the immutable fundamental principles. The premises are that a small set of fundamental principles (conservation of energy or loop rule, conservation of momentum, conservation of charge or node rule, Maxwell’s equations, etc.) fully explain all concepts across multiple disciplines. For example, a school of fish can be conceptualized as a result of Hooke’s law (|~F |=−k∆x), where fish experience two forces, one is that they like to stay around other fish, at the same time avoiding other fish. The different shapes of schools of fish are related to different spring constants k, which represent the material. A solid understanding of

http://groups.physics.umn.edu/physed/Research/CGPS/GreenBook.html
1.3 Team Work 11

springs therefore helps understand aspects of fish in biology. Using the same example, the concept is extended to Electricity and Magnetism, where a capacitor can be understood in a similar way as a spring. The maximum displacement ∆x or amplitude A is compared with the charge Q and the inverse of the spring constant is compared with the capacitance C. In this sense, then capacitors reappear as an old concept related to springs and an expert quickly understands what happens to a configuration of capacitors in series, given the framework from springs. Therefore, training for the recognition of analogies is crucial in conveying the importance of physics in everyday life. Hence, problem solving in physics is based on a method than can be trained and learned. The first step in problem solving is "understanding the problem"; the problem solver resolves this step by paraphrasing the problem and drawing a sketch that includes all important variables in his/her own language. The paraphrasing should reuse the least possible wording images from the given problem. About 20 – 35% of the points are awarded for this practice. In the next step, the problem is "classified"; i.e. you identify the relevant broad principles and definitions of quantities associated with the problem. This step is given 20 – 25% of the score. At this point, you should be able to execute the problem by modifying and adapting the principles and definitions to the specifics of the problem and solving for unknown quantities. This step is scored 15 – 30%. In the last steps, verification that the units are carried in all steps, vectors are properly marked, answers are clearly, either as magnitudes or as vectors. This step receives about 5 – 10% of the score. At last, the answer is spelled out in a sentence that clearly answers all questions that were asked. You also check whether the answer makes sense, relates to anything that you know (being skeptical). This part is attributed about 10 – 20% of the full problem score. More details and examples are provided in section 3 on page 21.

1.3.3 Discussion Forum You will receive an invitation to participate in the discussion forum. Once, you accept it, you create a username, which will be the name listed for your postings (so do not use your student ID), but rather your first name or something simple. The discussion forum has two main sections, one for team tasks and another section for showcases. As a first step, familiarize yourself with the discussion forum, find your team members, and your assignments. The team leader will create a task in the forum, and members of the team will participate in the discussion to solve the particular task. Regular postings will be useful and are called "team posts". Aside from "team posts", you are also encouraged to make "peer posts" in threads run by other teams. You can also post images from your phone, dropbox, social media, and share your diagrams, sketches, and ideas you have on paper. Make sure to only include your own images, as other images may infringe copyright laws; the same is true for text, any amounts of text that exceed one sentence should be linked, rather than copied or paraphrased. Posting inappropriate and/or copyrighted content may result in getting permanently banned from the site with no possibility to make up further points for team tasks. The feed-back includes sentences, such as "did you think of . . . ", "I found section . . . in the book useful in respect to this problem as it explains", "a good application of this problem would be . . . ", "this problem makes me think of . . . ", and "In the book, I found . . . ", etc. For some students, solving problems is easy, for other asking questions is easy. Both are equally important in this task. Asking questions is particularly useful as it provides peers the opportunity to respond. Remember that team work is difficult, but also rewarding. Even though, you may think that you understand something, once you put the physics in writing, conceptions can be clarified.

1.3.4 Bloom’s taxonomy The educational benefits to team work stress that several learning levels of Bloom’s taxonomy can be integrated.[1] According to B. Bloom learning is based on the taxonomy that includes 6 aspects: • remember: memorize fundamental relations, such as ~F = 14πε0

Q1Q2 r2 r̂

12 Chapter 1. Introduction

• understand: what do the variables mean in the fundamental relations? What is r and Q1, can you make a drawing that explains it? • apply: can you solve a problem with Coulomb’s law? • analyze: how is Coulomb’s law different and the same to the gravitational law? • evaluate: what kind of charge distributions can be solved with Coulomb’s law? • create: can you synthesize a problem that involves Coulomb’s law?

You notice that the difficulty increase as you step through the taxonomy. A good learning style includes several or all of these aspects.

2. Lab Report Guidelines

THE following is an outline of the requirements and recommendations for a well-written labreport in the Electricity and Magnetism course. Please note that scientific writing is an important skill and your peers and instructor will be evaluating your lab report and provide you with feedback. The report has the specific purpose of giving a third-party (peer, instructor) an organized communication piece of your experiment, so that they can learn about what has been done, what was found, what the meaning of the results are, and so that they could redo the experiment themselves.

2.1 Online Lab Organization

An experiment has roughly the following sequence, which is based on the real-world process for scientific discovery:

1. Request for proposal (RFP), the experiment should be clear, include a hypothesis, computa- tion, and prediction.

2. Specify your prediction. 3. Assemble all pieces required for the experiment. 4. Perform the experiment, and note every detail in your lab notebook. 5. Write the Lab Report 6. Submit your Lab Report 7. Receive feed-back from the instructor and peers. 8. Evaluate Lab Reports from your peers to become better writer. 9. Reflect on the received feedback.

2.2 Report Structure

The lab report should have the following structure, which is common in the scientific literature. Many examples are available at the e-print archives (https://arxiv.org/):

1. Title 2. Author

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14 Chapter 2. Lab Report Guidelines

3. Affiliation, Date 4. Abstract (one paragraph) 5. Introduction (overview and purpose) 6. Experiment (explain how the experiment is performed) 7. Results (list your specific results, include a table) 8. Analysis (explain what the results mean, include a graph) 9. Summary (one paragraph), sometimes called conclusion

10. Acknowledgments (any help received) 11. Bibliography (any references)

An example for the Title is "Lab 1: Number of Electrons Removed in Tape". Titles such as "experiment 1" are not descriptive of the text. The title should reflect the outcome of the report in a succinct way. The author is your full name. The affiliation is the school’s name including the department. The date is added after the affiliation. Important: In the scientific lab report, passive voice is generally accepted. If active voice is used, the royal we is used: "we", when referring to yourself. The experiment should be conducted by yourself, however, if you have collaborated with others, then you need to include the names of the collaborators in the acknowledgement along with their clear contribution. Any work that is not quoted and cited is assumed to be your work. If the report contains more than 10% of work from other’s (including wikipedia) that is not quoted or properly cited, then the report is considered incomplete and no points are awarded. The report should be an original piece of work. The Abstract is written only after the report has been finished. You should keep a placeholder and then come back. It is always one paragraph, or 3 – 5 sentences. It is a brief summary, such as ?Using electrostatics, the number of electrons that can be removed from a common piece of tape was measured. Using a neutral piece of tape and a charged piece of tape, we determined the farthest distance of interaction to be 4(1) mm, which corresponds to a charge of Q = -40(10) nC (or 250 billion electrons). The charge was determined from the distance using an electrostatic model of interaction between a charge and a neutral object.? The abstract should include the final numbers and be very specific. A common mistake is to confuse the abstract with the introduction. These are very different parts. Also, commonly, we use the notation 4(1) to mean that the measured results have a confidence of 67% to lie within 3 – 5 mm. So 4(1) = 4±1 mm. Make sure that you include units. Keep the abstract succinct. The Introduction includes an overview. It generally includes material from the book. The relevant information about Coulomb?s Law, interactions between a charged and a neutral object, where the force decays as 1/d5, where d is the separation distance. Importantly, this is the section where you must include your prediction. The Experiment includes the specific procedure that you used to make the measurement. Ideally, you would include a photo of your setup and then explain it in about two paragraphs. The Results include a table with the measured results and a paragraph of what the results are. "In table 1, the distance d is listed for 5 experimental runs". The Analysis part states your final answer and makes a comparison with the prediction. Note here, that if you do not have a prediction, then you cannot analyze anything. That is the reason it is so important to have predictions ready. Of course, the predictions can be off from your experimental results. It is important that you include the original predictions. If you realized that in the predictions you forgot to include a component, then you can explain this. The Summary is a one-paragraph summary of all that has been done. It is different from the abstract as it focuses on the analysis. The purpose of the abstract is to interest the reader in reading the full report. The purpose of the summary is to give a brief synopsis of what has been found. In the Acknowledgment section, you should include any other persons who participated in the experiment, or contributed in any way.

2.3 Report Submission 15

Figure 2.2.1: Experiment with charged straw. When the charged straw is (a) far from the uncharged mass, the force to lift it is too weak. However, at a distance of 8 mm, the attractive force overcame the gravitational pull and sticks to the charged object (taken into account the offset at the bottom of the ruler). This is a sample photo for lab reports, showing the name and date on the post-it in the background.

In the Bibliography section, you should include any relevant references. Some students choose to use Zotero plugin to simplify citations and produce professional references.

2.3 Report Submission

Your report should include a photo of the experiment (including the date stamp and name), a table for your results, and a graph from the analysis. Commonly, you would use a MS Word, Google Docs, OpenOffice Writer, or LaTeX (https://www.sharelatex.com/, https://www. overleaf.com/) to write your report. Please submit the Word document, or if needed PDF- converted document to the DropBox on Beachboard.

2.4 Grading Rubric

Each report is graded. The following criteria are generally applied in grading your lab reports (100 points = 100%).

1. (10pts) Are all predictions from the lab assignments included in the report? (not graded on correctness, but completeness only, as predictions can be different from experiment)

2. (10pts) Is it complete? Does it have all the structural elements? (see section 2.2) 3. (10pts) Does the abstract convey the main results succinctly in one paragraph? 4. (10pts) Is there a good experimental image with the date and name of the author? (see

Fig. 2.2.1) 5. (10pts) Does the report include a data table? 6. (10pts) Does the report include a graph with a long caption? 7. (10pts) Is there a summary that includes all main results? 8. (10pts) Are correct SI units used throughout the report? 9. (20pts) Do the results make sense, and was proper language used in the report, is the report

unique, interesting, and complete?

2.5 Measuring Data

For precise measurements, images are captured with the phone and then analyzed with software. An easy and freely available software for multiple platforms is NIH ImageJ at https://imagej.

https://www.sharelatex.com/
https://www.overleaf.com/
https://www.overleaf.com/
https://imagej.nih.gov/ij/
https://imagej.nih.gov/ij/
16 Chapter 2. Lab Report Guidelines

nih.gov/ij/. The software allows you to calibrate the image; i.e. define a known distance on the ruler. From the menu choose "Analyze", then "Set Scale". Apply the units, for the report all units should be SI units; i.e. meters, millimeters (mm), and so on. After the calibration you can easily read of distances in the proper units. You can also measure areas.

2.6 Ethics Ethical behavior is utmost important. Plagiarism is not accepted as a policy by the University and ramifications are listed on the University page for "Cheating and Plagiarism" (http://web.csulb. edu/divisions/aa/catalog/current/academic_information/cheating_plagiarism.html). What are some of the important things to know for this course. Individual reports must clearly identify the contributions of others in the acknowledgments and throughout the text by using quotes, references, and proper wording. During the experimental conduct, cooperation is acceptable, ques- tions, and support to make the experiment successful are acceptable as long as there are significant contributions. The lab report is an individual account What is ethics in the Sciences? Ethical behavior has a long tradition in science, mathematics, and engineering. It is necessary for its continuation. Misconduct in science centers around reporting research results that are fabricated, plagiarized, and or falsified, see http://www.aps. org/programs/education/ethics/.[6] Proper conduct includes • truthful, careful handling and reporting of data, • responsible, respectful interactions with peers and subordinates, • adherence to journal publication guidelines, including proper recognition of research contri-

butions. The American Physical Society publishes the "APS Guidelines for Professional Conduct" (https: //www.aps.org/policy/statements/02_2.cfm) with the goal to advance and diffuse the knowl- edge of physics.

2.7 Experiments Not all experiments "work", see discussion during Office Hours. Therefore, if your experiment does not yield results, please document the steps that you have taken to make the experiment work and the limitations that you have found. It is important to submit your effort for partial points. Include images of the experiment. Many scientists, mathematicians, and engineers draw valuable information from experiments that did not fully "work", as lessons can still be learned. Sometimes, experiments are designed with the purpose of showing nothing, these are called null experiments.

2.8 Arduino You can learn about the Arduino micro-controller at https://www.arduino.cc/. There are videos, resources, and tutorials available. After installing the software on your computer, you would test the Arduino board, generally by running the "blinking LED" program, see Listing 15.1 on page 80. After loading the program, you choose the Board. From the menu, select "Tools", then "Board". The second item is that you need to select the USB port. Go to "Tools", then select "Serial Port" and choose your USB connection. Next upload the program and watch for any errors. The Arduino allows you to connect sensors, such as temperature sensor, light sensor, and others, but also to control devices, such as LEDs, motors, and so on. The operating voltage for input and output is generally 5 V. The input voltage is analog, so it is converted to a digital signal using an analog-to-digital converter (DAC). The digital signal can be sent back to the computer and monitored via the so-called "Serial Monitor".

https://imagej.nih.gov/ij/
https://imagej.nih.gov/ij/
http://web.csulb.edu/divisions/aa/catalog/current/academic_information/cheating_plagiarism.html
http://web.csulb.edu/divisions/aa/catalog/current/academic_information/cheating_plagiarism.html
http://www.aps.org/programs/education/ethics/
http://www.aps.org/programs/education/ethics/
https://www.aps.org/policy/statements/02_2.cfm
https://www.aps.org/policy/statements/02_2.cfm
https://www.arduino.cc/
2.9 Fitting Data 17

After you compiled the program and sent it to the Arduino. You can open the Serial Monitor by clicking on the top right most button in the Arduino IDE labeled "Serial Monitor" and represented by a looking glass. It will open a new window with the output from the board. You can see an ex- ample listed at https://learn.adafruit.com/adafruit-arduino-lesson-5-the-serial- monitor/overview.

2.8.1 Breadboard

The Arduino kit often comes with a breadboard and wires which will be very helpful. If you are unfamiliar with a breadboard for circuit compilation, then refer to tutorials on the web, or at https://learn.sparkfun.com/tutorials/how-to-use-a-breadboard. In general, a bread board has two parallel long lines for ground and positive voltage (5 V); then it has horizontal rows of 5 pins each. Each of the 5 pins are at the same potential, on the back of the board, they are connected.

2.9 Fitting Data

Scientists, mathematicians, and engineers often use models and compare them with experimental data. The model also allows the experimentalist to extract specific information. For example, in the lab on magnetic fields (chapter 14 on page 77) you can determine the magnetic moment from fitting the magnetic field data to a dipolar model. Fitting data is certainly a useful and valuable (think CV, resume) skill, but it is not necessarily easy. Fortunately, there are some tricks of the trade. If you can fit a line with the equation y = mx+b and determine the slope m as well as the offset b, then you can take more complex functions and linearize them. One example of this strategy is explained on page 14.4. In this case, a power law can be plotted on a log-log graph and the exponent is revealed as the slope, the pre-factor is buried as the offset. For another type of common equation, an exponential function, such as those used in the RC lab (chapter 18 on page 87) would be graphed on a semi-log plot and the slope is proportional to the time constant. The specifics can be derived in the same fashion as shown page 77 for the power law. Using brute force, the less mathematically inclined person, would using a fitting program and simply take the data and fit a particular function corresponding to the model. Common programs include Excel and RStudio (open source) based on R language. The following advanced example provides code to make a fit using R and is intended for the enthusiastic reader and should be considered optional. In the first part, the data is loaded from a file generated by the Tektronix oscillator, which is in a comma-separated format. The command to load the data into a data frame is called read.csv.

# Loading data from Tektronix oscilloscope data <- read.csv(’data.csv’, header=FALSE) names(data)[4:5] = c(’time’,’V’) # label columns data$time = data$time*1E3 # convert s to ms q = subset(data, time < -0.1) # correct for offset data$V = data$V - mean(q$V)

This data frame contains two columns labeled time and V, which contains the time in units of ms and the electric potential measured in units of V. A graph is generated by first invoking plot to generate the data points. A second layer is added with the command points in order to high light the data points that will be used for the fit.

https://learn.adafruit.com/adafruit-arduino-lesson-5-the-serial-monitor/overview
https://learn.adafruit.com/adafruit-arduino-lesson-5-the-serial-monitor/overview
https://learn.sparkfun.com/tutorials/how-to-use-a-breadboard
18 Chapter 2. Lab Report Guidelines

−0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

0. 0

0. 5

1. 0

time(ms)

V (V

)

Figure 2.9.1: Measurement of a free induction decay from protons in glycerin. The graph is generated with R, where data points (circle) represent voltage measured after a 90o pulse was applied to create precession. The relaxation of the signal amplitude is modeled and fit with an exponential decay (see text on page 18).

plot(data$time, data$V, xlab=’time(ms)’, ylab=(’V(V)’), ylim=c(-0.2, 1.3), xlim=c(-0.5, 3))

d <- subset(data, time>0.3) # fit subset of data points(d$time, d$V, col=’red’)

R provides a straight-forward way to make a non-linear fit to the data using the command nls, which takes 3 main parameters. The first parameter is the data frame that contains the data to be fit. Next the model is described, which is V = Aexp[−time/T ], where A and T are fitting parameters, and the others are variables defined in the data frame. The fit will only work, if reasonable starting fit parameters are provided. The starting parameters are provided in the form of a list. The result of the fit is stored in a variable called fit. The fit line is added to the plot by using predict to compute values along some time values. In this case a vector with 100 elements is generated, the time running from 0 to two times the maximum. The fit is overlaid using blue color and line thickness of 4. The result of this code is shown in Fig. 2.9.1.

# do fitting, giving some reasonable starting values nls(data = d, V ~ A*exp(-time/T), start=list(A=1, T=1)) -> fit time.fit = seq(from =0, to =max(d$time)*2, length.out=100) predict(fit, list(time=time.fit))->V.fit time.fit=c(-1,0,time.fit) V.fit = c(0,0, V.fit) lines(time.fit, V.fit, col=’blue’, lwd=4)

It is noteworthy that plot will clear the graph, but you can still add data later using either lines or points for adding data with a line or data points, respectively. The fitting parameters can be separately listed with summary(fit)$coeff. The same plot can also be graphed with the previously mentioned ggplot2 package. A common way to use ggplot is to make a table with three columns (using melt package for complex data). The first column is the x-axis, the second the y-axis, and the third column defines the data set for which automatically a legend is displayed. In the following example, the NMR FID data is

2.9 Fitting Data 19

appended to the fitting data, by using the row binding function rbind. The third column is called label and is filled with the label for each row. The command length returns the number of items in a vector and nrow returns the number of rows of a data frame. Finally, the axes are labeled and the title of the legend, which would be "label", is hidden. The legend.key element defines the square around each of the items in the legend.

myData = data.frame(time = time.fit, V = V.fit) myData = rbind(myData, cbind(time = data$time, V = data$V)) myData$label = c(rep(’fit’,length(time.fit)),

rep(’data’, nrow(data))) ggplot(myData, aes(time, V, color=label, linetype = label)) +

geom_line(size=2) + theme_bw(base_size=22) + xlab(’time (s)’) + ylab(’V (V)’) + scale_y_continuous(limits=c(-0.2,1.4)) + scale_x_continuous(limits=c(-0.8, 2.6),

breaks=seq(-0.5,2.5,0.5)) + theme(legend.position = c(0.1, 0.9),

legend.title = element_text(color=NA), legend.key = element_rect(colour = NA))

3. Practice Exams

PHYSICS is a fundamental science that stresses immutable laws that describe nature under themost varied conditions. Therefore, the application of these fundamental principles to diverse problem sets in the real world is an imminent goal of the course. It is widely recognized that physics has applications in all fields of science, engineering and beyond. The exams are guided by the student learning outcomes defined in the syllabus and problem solving skills, see grading in section 1.3.2. Exam problems should be approached strategically in order to maximize the score. The following steps convey the logical procedure in problem solving.

1. Understanding the problem by providing your own sketch, diagram, and picture of the problem, which includes variables that are relevant to the problem.

2. Application of a principle by categorizing the problem to a particular ummutable law that is applicable to the problem. This are generally principles of conservation (Node Rule, Loop Rule, charge conservation, energy conservation, momentum principle, . . . ) or fundamental ideas (Faraday’s Law, Coulomb’s Law, Superposition Principle, . . . ), and sometimes also include definitions (I ≡ dQ/dt, . . . )

3. Execution of the problem by applying the principle to the specific problem and calculating a new result.

4. Skeptical analysis of the problem including the verification of the units, whether the result makes sense, whether all questions have been answered, and how the result can be interpreted within the broader context of the problem.

3.1 Problem with Solution Problem: A balloon of radius 12 cm carries a uniformly-distributed negative charge of -6 nC on its outer surface. An uncharged solid metal block is placed nearby. The block is cubic and 6 cm thick. The left side of the metal block is 10 cm away from the surface of the balloon. (a) Draw a clear sketch with the induced charge distribution on the met al block. Note a 2D sketch (circle + square) will be sufficient. (b) Calculate the electric field at the center of the metal block due to the charges on the block only. Solution: see Fig. 3.1.1 on page 28.

22 Chapter 3. Practice Exams

3.2 Midterm Practice Problems

Instructions: Clearly state your entire solution path, solution must be derived from fundamental principles. Full or partial credit will only be given for clear steps. Correct final result is not sufficient for full points, diagrams, concepts, and mathematical derivations must be included. Units must be provided or points will be subtracted. Clearly label the end result, use double lines to underscore or box in the final result. Any form of plagiarism will result in zero score. Problem 1: A small bar magnet (2 cm in length) made of nickel has a magnetic dipole moment, such that it produces a magnetic field of 5 mT at a distance of 25 cm from its center. At what distance would the magnetic field be 8 mT? Problem 2: The following circuit has 3 resistors, where R1, R2, R3. The first two resistors R1 and R2 are connected in parallel. The pair is in series with the third resistor and the battery, which provides a constant electric potential of emf. (a) Draw the circuit (at least use 1/3 of the page). Clearly label the currents. (b) Choose two independent loops (indicate direction and number in the diagram). Write two equations from the loop rule corresponding to your diagram. Write one equation with the currents using the node rule. (NOTE: points will only be provided, if you currents and loops are labeled with arrows and clear labels.) Problem 3: In the circuit below, the connecting wires are much thicker and have much higher mobility and electron density than the filaments in the light bulbs. The length of the filament in the "long" bulb (top branch) is same as the "round" bulb (lower branch). They are made of the same material, and therefore have the same electron density and mobilities, see Fig. 3.2.1. (a) If electron current i2 = 2.9×1018 electrons/s, and i3 = 4.1×1018 electrons/s, what is the electron current through the i1 through the long bulb? Answer the following multiple choice questions about the circuit. For each question, circle the best answer AND provide an explanation. (b) The magnitude of the potential difference across the long bulb is:

1. greater than the magnitude of the potential difference across the round bulb 2. less than the magnitude of the potential difference across the round bulb 3. equal to the magnitude of the potential difference across the round bulb 4. not enough information to determine

Explain: (c) The magnitude of the net electric field in the filament of the long bulb is:

1. greater than magnitude of the electric field in the round bulb filament 2. less than the magnitude of the electric field in the round bulb filament 3. equal to the magnitude of the electric field in the round bulb filament 4. not enough information to determine

Explain: (d) The cross sectional area of the filament of the long bulb is:

1. greater than cross sectional area of the round bulb filament 2. less than the cross sectional area of the round bulb filament 3. equal to the cross sectional area of the round bulb filament 4. not enough information to determine

Explain: Problem 4: An electron is accelerated from rest at a position of 30 cm away from the center of a charged balloon. The balloon has a radius of 12 cm and has a positive charge of 50 nC. Calculate the speed of the particle when it hits the balloon. Problem 5: You place a long straight wire on top of your compass, and the wire is a height of 2 mm above the compass needle. If the conventional current in the wire is I = 0.7 A and runs left to right, calculate the approximate angle the needle deflects away from North and draw the position of the compass needle.

3.3 Final Exam Practice Problems 23

3.3 Final Exam Practice Problems Problem 1: A circuit with 3 resistors is connected to two 4.5 V batteries. The two batteries are in series. Two resistors with 50 and 80 Ω are connected in series and then connected in parallel to the third resistor, which is 200 Ω. Draw the circuit and label the resistors R1, R2 and R3. Then, calculate the power consumption of the 50 Ω resistor. Problem 2: A plane electromagnetic wave is given by the following equations with E0 = 1 V/m.

~E = 2E0ẑsin (

2π λ

y+4π×1015t )

~B = ~B0 sin (

2π λ

y+4π×1015t )

(a) (3 pts) What is the velocity of the propagating wave (direction, magnitude)? (b) (3 pts) What is ~B0 (magnitude and direction)? (c) (4 pts) What is the wavelength λ of the wave (in units of meters)? Problem 3: An electron is accelerated from rest through a potential difference of 2.5 kV applied to two capacitor plates. (a) (5 pts) What is the resulting speed va? (b) (5 pts) The electron then travels horizontally~v =< va,0,0 > and hits a 20 cm long tube with a vertical electric field of < 0,−2000N/C,0 > . What will be the final velocity (vector!) after exiting the tube? Problem 4: There are two current-carrying wires that go from the floor to the ceiling. The ceiling is 3 m above the floor. The wires are parallel to each other and separated by 20 cm. You know that both wires carry the same amount of current and the magnetic field strength produced by the wires at the mid-point between the two wires is 50 µT. (a) (4pts) Calculate the current in each of the wires. (b) (2pts) Are the currents running parallel or antiparallel to each other? Explain. Problem 5: A circular coil of radius 6 cm has 200 turns and a total resistance of 3 Ω. Initially, it is placed in a region with a uniform magnetic field of 2.5 T perpendicular to the coil area. (a) (5 pts) You hit a switch and turn off the magnetic field and within 50 ms, the magnetic field completely disappears. Find the average emf that is induced in the coil? (b) (5 pts) Using energy considerations and power, how much work is needed to remove the coil from out of the magnetic field. (You may use the answer from part (a) to answer this question). Problem 6: A very long wire carrying a conventional current of 3.1 A is straight except for a circular loop of radius 5.4 cm. Calculate the approximate magnitude and the direction of the magnetic field at the center of the loop. Include a coordinate system in your drawing. Problem 7: A compass originally points North. A bar magnet is aligned East-West, pointing at the center of the compass. When the center of the magnet is 0.23 m from the center of the compass, the compass deflects 70◦. What is the magnetic dipole moment of the bar magnet? Problem 8: You have 3 light bulbs and one battery. All 3 light-bulbs are exactly the same. Build three circuits, A) one circuit, such that the light-bulbs output the most light, B) with the least output, but still using all three light-bulbs in the circuit, and C) an intermediate circuit that shines light with more intensity than the dimmest and less than the brightest. If circuit A drains the battery completely in 2 hours, how long will the battery last for circuits B) and C) ? Problem 9: A charged solid sphere at the center and 2 charged hollow spheres produce an electric field. The charge q is 20 nC and the solid sphere contains a positive charge that is 60 nC, while the hollow spheres contain negative charges of -20 nC each. Using Gauss’ Law, find the magnitude of the electric field at each of the following points M, N, and O, which are located at 5 cm, 7 cm, and 10 cm away from the center. The inner sphere has a radius R=4 cm, the next ring is located at r=6 cm, and the final ring is at s=8 cm.

24 Chapter 3. Practice Exams

3.4 Basic Relations in Electricity and Magnetism You should memorize the following relationships and definitions. It is a step to make you an effective problem solver and you can also do well on general tests, such as MCAT, GRE, EIT, and others. Some have argued that memorization is unnecessary as they can be looked up. Experts disagree and confirm that memorization of these fundamental principles allows you to apply them broadly. Those are your tools in solving problems and merely being able to look them up is insufficient to sophisticated recognition. Practice writing the equations on a piece of paper, after you have learned the concept from the chapter.

Maxwell’s Equations

Gauss Law (Electricity): ∫�� ��∫ ~E ·d~A = 1

ε0 Qencl. for any closed surface

Gauss Law (Magnetism): ∫�� ��∫ ~B ·d~A = 0 for any closed surface

Ampère-Maxwell Law: ∮ ~B ·d~l = µ0Iencl.+µ0ε0

dΦel dt

with Φel = ∫∫

~E ·d~A

Faraday’s Law: ∮ ~E ·d~l =−

dΦmag dt

with Φmag = ∫∫

~B ·d~A

Lorentz Force ~F = q~E +q~v×~B d~F = Id~l×~B (wire)

Coulomb ~E = 1

4πε0 q r2

r̂ Biot-Savart Law ~B = µ0 4π

q~v× r̂ r2

3.4 Basic Relations in Electricity and Magnetism 25

position vector:~r = r · r̂ =< x,y,z > ~r points from source charge to observation point force on charge: ~F2 = q2~E1

Superposition Principle Conservation of Electric Charge

Dipole: along axis: |~Eaxis| ≈ 1

4πε0 2qs r3

perp. axis: |~Eaxis| ≈ 1

4πε0 qs r3

for r� s

Electric dipole moment: ~p = q~s polarization: ~p = α~Eapp disk: E ≈ σ0

2ε0

( 1− z

R

) surface charge density: σ0 =

Q A =

Q πR2

capacitor: E ≈ σ0 ε0

∆V = σ0 ε0

∆x

electric potential: ∆V =Vf −Vi =− ∫ f

i ~E ·d~r ~E ·d~r = Exdx+Eydy+Ezdz

potential energy: ∆Uel = q∆V ∆V < 0, if path same direction as ~E

Energy Principle ∆Esys =Wsurr +Q, ∆Esys = ∆K +∆U , K f = 1 2

mv2f

dielectric constant K: ~Einsulator = ~Eapplied

K current: I =

dq dt

= |q|nAv̄ (units: A = Ampère)

wire: B≈ µ0 4π

2I r

(for r� L) loop (ring): B≈ µ0 4π

2µ z3

(for z� R), µ = IA

solenoid: B≈ µ0NI L

Node Rule (Iin = Iout) Loop Rule (∆V1 +∆V2 + . . .= 0)

conventional current: I = dQ dt

= |q|nAv̄ electron current: i = nAµE drift speed: v̄ = µE current density: j = I/A = σE

conductivity: σ = |q|nµ resistivity: ρ = 1 σ

, R = L

σA circular motion: ω =

v R = |q|B γm

Momentum Principle: F = mv2

R for circular motion

torque on magn. dipole: ~τ =~µ×~B potential energy of magn. dipole: Umag =−~µ ·~B

Hall effect: ∆VHall = E||h = v̄Bh = IBh |q|nA

26 Chapter 3. Practice Exams

resistor: ∆V = IR (Ohm’s Law) capacitor: ∆V = Q/C

Power: P = dW dt

= I(∆V ) inductor: ∆V = L dI dt

parallel resistors: 1

Requiv. =

1 R1

+ 1

R2 +

1 R3

series: Requiv. = R1 +R2 +R3

parallel capacitors: Cequiv. =C1 +C2 +C3 series: 1

Cequiv. =

1 C1

+ 1

C2 +

1 C3

Series RC circuit: I(t) = em f

R e−t/RC charge: Q(t) =C · em f (1− e−t/RC)

self-inductance (solenoid): L = µ0N2

d A flux through solenoid: Φ =

µ0N2

d AI

energy volume

= 1 2

ε0E2 + 1

2µ0 B2

Radiative ~E-Field: ~Erad = 1

4πε0 −q~a⊥

c2r E = cB in phase for EM radiation

EM radiation speed: c = 1

√µ0ε0 = 3×108m/s direction of~v is ~E×~B

Poynting vector: ~S = 1 µ0

~E×~B units of W/m2

milli m 1×10−3 kilo k 1×103 micro µ 1×10−6 mega M 1×106 nano n 1×10−9 giga G 1×109 pico p 1×10−12 tera T 1×1012

3.5 Reference This part does not need to be memorized.

uniformly charged thin rod E = 1

4πε0 Q

r √

r2 +(L/2)2 B =

µ0 4π

LI

r √

r2 +(L/2)2

uniformly charged ring E = 1

4πε0 qz

(R2 + z2)3/2 B =

µ0 4π

2πR2I (R2 + z2)3/2

uniformly charged disk: E = σ0 2ε0

( 1− z

(R2 + z2)1/2

) rel. factor: γ =

1√ 1− v

2

c2

3.5 Reference 27

magnetic constant µ0 4π×10−7 Tm/A electric constant ε0 8.85×10−12 C2/Nm2 speed of light c 3×108 m/s Gravitational constant G 6.7×10−11 Nm2/kg2 electron mass me 9×10−31 kg proton mass mp 1.7×10−27 kg neutron mass mn 1.7×10−27 kg Earth mass ME 6.0×1024 kg Earth radius rE 6.37×106 m Sun mass MS 2×1030 kg electron charge e −1.6×10−19 C Avogadro’s number NA 6.02×1023 atoms/mol

28 Chapter 3. Practice Exams

Figure 3.1.1: Solution to Problem on page 21 with points attributed to different portions of the solution. The full number of points for this problem is 10 points; this is the first part of the problem. The diagram should be large enough to capture small details that you add and always include labeled coordinate axes.

3.5 Reference 29

Figure 3.2.1: Diagram for problem 4 showing two batteries connected to two light bulbs.

I 4 Activity 14: Electric Fields . . . . . . . . . . . . 334.1 Objective4.2 Background4.3 Prediction: Charge Configurations4.4 Calculation4.5 PHeT Simulation5 Activity 15: Electric Field Hockey . . . . . 375.1 Prediction 5.2 PhET simulation 5.3 Evaluation

6 Activity 16: Electric Potential . . . . . . . . . 41 6.1 Prediction 6.2 Simulation 6.3 Evaluation

7 Activity 17: Electric Field from Irregular Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

7.1 Background 7.2 Prediction 7.3 Calculation 7.4 Evaluation

8 Activity 18: Light Bulbs . . . . . . . . . . . . . . . 47 8.1 Prediction 8.2 Mesaurements 8.3 Evaluation

9 Activity 19: RC Circuits . . . . . . . . . . . . . . . 53 9.1 Background 9.2 Predictions 9.3 Measurements 9.4 PhET Simulation

10 Activity 20: Series and Parallel Resistors 59 10.1 Series Circuit in a Parallel Circuit 10.2 Parallel Circuit in a Series Circuit 10.3 Series Circuit in a Parallel Circuit in a Series Circuit

11 Activity 22: Faraday’s Law . . . . . . . . . . . 63 11.1 Background 11.2 Bar Magnet 11.3 Electromagnet 11.4 Pickup Coil 11.5 Transformer 11.6 Generator

12 Activity 23: Radio Waves . . . . . . . . . . . . . 69 12.1 Prediction 12.2 Simulation

Interactive Simulations

4. Activity 14: Electric Fields

How it works: follow a particular routine for all activities, see section 1.1. First familiarize yourself with the background information from the chapter (found in the textbook[2]); next note your predictions in writing. It is crucial that you make a prediction before you perform the activity, as only then you will be able to evaluate the activity. The prediction is based on your best knowledge and not on a guess. If you guess, it is not a prediction, and you should review the chapter in the textbook first. A prediction is based on knowledge.

4.1 Objective

This activity explores electric fields based on different basic charge configurations. The simulation is at http://phet.colorado.edu/en/simulation/charges-and-fields.

4.2 Background

All common matter is made of atoms, which contain positive and negative charges. Charges manifest themselves by creating an electric field. Other charges can interact with the electric field that are produced. Even though, most atoms are neutral; i.e. the number of positive charges (protons) and negative charges (electrons) is equal, they still produce an electric field due to the exact positions, see dipolar fields. An electric charge (positive or negative) creates an electric field that permeates all of space as it propagates at the speed of light (of that medium) through all of space. Another charge appearing in this space is affected by that field and experiences a force. In this scenario, the two charges do not directly interact with each other (in the sense that you are used to with mechanical collisions); one charge creates a field and the other charge interacts directly with that field. The direction of the electrical force on a charge is along the direction of the field. It is noteworthy that field lines and field vectors are different. Note that a vector such as ~E corresponds to one particular point in space. It is a vector, therefore a straight line. On the other hand, field lines are sometimes drawn to assist you in drawing the field vectors, which are tangent to the field lines. The field lines emanate from positive charges and drain into negative charges. The electric field

http://phet.colorado.edu/en/simulation/charges-and-fields
34 Chapter 4. Activity 14: Electric Fields

vectors are tangent and have a magnitude, which is not observed in the field lines. It is best to use electric field vectors as the field lines are not always an accurate representation.

4.3 Prediction: Charge Configurations Pick three charge configurations involving one positive charge, one negative charge, two positive charges, and two charges with an opposite polarity. You will select the magnitude for these charges. Q1: Make a sketch. Using your understanding of electric forces and electric fields, draw the electric field lines for all of these configurations. At this point you are not making any calculations, but you are making predictions about how the electric field around the charges will look. While you are making these predictions, please do not reference the internet or your textbook. Q2: Draw the field lines for the isolated charges below. Make sure you are sketching continuous field lines.

Positive Charge

A

Negative Charge

B

Two Like Charges

C

Two Unlike Charges

D

Q3: What is the difference between a field line and a field vector?

4.4 Calculation 35

4.4 Calculation In this part, you are going to compare your prediction by verifying the electric field lines using vectors. Make sure to specify the amount of the charge and the distance between the charges. You will also need to use a small positive test charge. Q4: Calculate the electric field resultant vector on the positive test charge at different points in the field. Perform the calculations at a minimum of at least four points for each configuration. Q5: Use a grid (Fig. 4.4.1) to accurately draw field vectors for both single charge configurations.

Figure 4.4.1: Accurate drawing of field lines.

Use a grid (Fig. 4.4.2) for both single charge configurations.

4.5 PHeT Simulation Q6: Use the computer simulation to further confirm your hypothesis and/or your calculations. Access the "Charges and Field" simulation package from PHeT. Make sure to select "Show E-Field". The E-Field sensor acts similar to a positive test charge. Does the simulation agree with your findings? Include a screenshot. Q7: Explain.

Q8: Reflect on your learning What I observed during the simulation:

36 Chapter 4. Activity 14: Electric Fields

Figure 4.4.2: Accurate drawing of field lines.

Q9: What connections I made:

Q10: What I now understand:

Q11: What I still wonder about:

Q12: Finally: find at least two applications of electric fields and explain how they work.

5. Activity 15: Electric Field Hockey

This activity helps you explore the force of charge configurations on a charged particle. The Electric Field Hockey simulation is available at http://phet.colorado.edu/en/simulation/ electric-hockey.

5.1 Prediction

Consider the following 5 arrangements of charges, see Fig. 5.1.1. It may help to use the Electric Field Hockey Simulation to consider these arrangements, but notice that here the puck has a negative charge and can move; the other charges are fixed. You can change the charge on the puck in the simulation by checking the box at the bottom. When thinking about these arrangements, you should be sure to apply Coulomb’s Law. Q13: Consider the following statements about the configurations in Fig. 5.1.1.

TRUE FALSE All of the pucks feel a force to the right. TRUE FALSE The puck in C feels a greater force to the right than the puck in D. TRUE FALSE The puck in E feels a force to the right that is four times greater

than that felt by the puck in B. TRUE FALSE The net force on the puck in A is zero.

We can use the electric field hockey game to help us think about electrostatic forces (~F = Q~E) that are occurring in our everyday lives. Which one of the above charge distributions would be a helpful guide in thinking about the electrostatic forces in the following scenarios? Q14: a charged balloon (puck) sticking to the wall:

Q15: a charged sock (puck) sticking to a shirt:

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38 Chapter 5. Activity 15: Electric Field Hockey

Figure 5.1.1: Each line is an arrangement of a charges.

Q16: a charged dust particle (puck) in an air cleaner:

Q17: a corona discharge:

Figure 5.1.2 shows a charge arrangement that is effective at producing a goal for Level #1 on Electric Field Hockey (here the pink are plus charges and the green is the positively charged puck). The path of the puck is shown as the green dash.

Q18: Choose Level #3 in the PhET Simulation (Electric Field Hockey), sketch the problem, and make a prediction of where the charges should be placed to make the goal.

5.2 PhET simulation 39

Figure 5.1.2: Each line is an arrangement of a charges.

Electric Field Hockey Prediction

3

5.2 PhET simulation

Q19: Run the simulation and take screenshots of the results. Using your knowledge, construct the solution for level 3 with the help of the simulation and compare your solution with the prediction. Q20: What is different, and why?

5.3 Evaluation

Q21: What new thing did you learn after doing this activity?

40 Chapter 5. Activity 15: Electric Field Hockey

6. Activity 16: Electric Potential

This activity is to explore electric field based on different more advanced charge configurations. The simulation is at http://www.compadre.org/portal/document/ServeFile.cfm?ID=11443& DocID=2406

6.1 Prediction

Use 10 positive charges (each is 1.5 C) and form a line. The units for charge are Coulomb (C). Then draw (this is prediction, do not run the simulation yet!) the electric field vector at several locations. Next think about the electric potential and draw field lines of equipotential (where the electric potential is constant). Where is the electric potential large and where is it small? Q22: Use 5 positive charges (1.5 C each) and 5 negative charges to form two parallel lines (similar to a capacitor). Then draw the electric field vector at several locations. Next think about the electric potential and draw field lines of equipotential (where the electric potential is constant). Where is the electric potential large and where is it small? Choose a coordinate system, and compute the electric potential at 4 different locations, given that the charges are distributed as Table 6.1.1.

Table 6.1.1: Charge positions for a capacitor-like model.

Charge (C) X (m) Y (m) 1.5 -0.25 -0.25

-1.5 -0.25 0.25 1.5 -0.14 -0.25

-1.5 -0.14 0.25 1.5 -0.03 -0.25

-1.5 -0.03 0.25 1.5 0.08 -0.25

-1.5 0.08 0.25 1.5 0.19 -0.25

-1.5 0.19 0.25

http://www.compadre.org/portal/document/ServeFile.cfm?ID=11443&DocID=2406
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42 Chapter 6. Activity 16: Electric Potential

Table 6.1.2: Table for predicted values of the electric potential at your chose locations.

No x (m) y (m) V (N/m) 1 2 3 4 5 6

Q23: Predictions for 4–6 locations are entered in Table 6.1.2. Make sure that you are using the right units. Q24: Use 10 positive charges and form a ring. Then draw the electric field vector at several locations. Next think about the electric potential and draw field lines of equipotential (where the electric potential is constant). Where is the electric potential large and where is it small?

6.2 Simulation Now run the simulation: ejs_em_PointChargeElectricPotential.jar for all three scenarios. Make a sketch for each configuration for the equi-potentials (contour plot) for each of the configu- rations. (NOTE that you can change the number of charges by changing the N parameter, hit enter after you change it, so it turns white from yellow. Also, check the Table checkbox, you can move charges by changing the coordinates in the table). Explore all the parameters and the different ways you can graph. There is a help file as well. Q25: Include a screenshot from your work. Q26: Also measure the actual value of the electric potential (by clicking on the grid mark) at the 4 chosen locations and compare with your prediction. What do you find?

6.3 Evaluation Q27: Discuss the differences from the prediction, what is different, why?

7. Activity 17: Electric Field from Irregular Shape

Use a numerical computation to compute the electric field of any charge configuration. After completion of this activity, you will be able to simulate real-world problems using numerical tools explained in Chapter 17 of Matter and Interactions textbook.[2]

7.1 Background

According to Coulomb’s law a source charge Q creates an electric field E at any observing location. Applying the superposition principle, it is possible to compute an arbitrarily complex configuration, by dividing the charge distribution into small charges ∆Q and then summing them up vectorially.

∆~E = N

∑ i=1

1 4πε0

∆Qi r2i

r̂i (7.1.1)

Here, r̂i is the unit vector from the source charge ∆Qi to the location of the observer. Mathematically, this can be expressed as

r̂i = ~ri ri =

~rsource,i−~robs |~rsource,i−~robs|

(7.1.2)

7.2 Prediction

Q28: Predict the direction and relative magnitudes of the electric field from a uniformly charged object that is very thin at four different points marked by X. The shape is given below. The charge Q is 200 nC. Q29: Predict on how should you distribute point-charges? Make a sketch and show the positions of the ∆Qi.

44 Chapter 7. Activity 17: Electric Field from Irregular Shape

Figure 7.2.1: The dashed area represents a uniform charge distribution with the total charge Q. The red crosses mark points of interest, where you calculate the electric field.

Irregular Shape Point Charges

I

Q30: What happens to the electric field, if the number of point charges increases as the total charge Q is kept constant. • Will it point in a different direction? Yes No • Will it (a) increase, or (b) decrease in magnitude?

7.3 Calculation

Q31: Use an Excel Spreadsheet (or OpenOffice Calc), or VPython (see textbook) to (numerically) compute the electric field at the four locations based point charges in Table 7.3.1. Use a minimum of 100 point-charges that are uniformly distributed in order to compute the electric field at the four locations. Your solution should include screenshots of all relevant information in the spreadsheet and the results should be vectors. Q32: Capture a screenshot of your computation.

7.4 Evaluation

Q33: Compare your computed and predicted values. What differences did you find?

7.4 Evaluation 45

Table 7.3.1: Positions and electric field vectors at those observation points for the charge distribution shown in Fig. 7.2.1.

No x (m) y (m) Ex (N/m) Ey (N/m) |E| (N/m) 1 2 3 4

Q34: What did you learn in this activity?

8. Activity 18: Light Bulbs

You learn about light bulbs, which are essentially thin wires.The simulation is at http://phet. colorado.edu/en/simulation/circuit-construction-kit-dc • Understand light bulbs in the context of thin wires and large resistors, • Build circuits from schematic drawings, • Use an ammeter and voltmeter to take readings in circuits, • Provide reasoning to explain the measurements and relationships to circuits.

8.1 Prediction

Q35: You have 3 batteries each is 1.5 V. If you put them in series and measure the voltage across, what will you measure? Fill out Table 8.1.1. Q36: Draw a circuit with 3 light bulbs in series and 3 bulbs in parallel and create one more configuration using three light bulbs and a battery. Which light bulbs are going to be the brightest, which one’s the dimmest, rank them by brightness, mark them Table 8.2.1.

Figure 8.1.1: Batteries arranged in series.

Table 8.1.1: Batteries in series.

Battery Voltage (V) 1+2 1+2+3

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48 Chapter 8. Activity 18: Light Bulbs

Series

A

Parallel

B

Your Design

C

Table 8.1.2: Draw a circuit with the 3 light bulbs in series, parallel, or your own combination. Use a similar battery for each circuit and indicate the relative brightness of each bulb.

8.2 Mesaurements 49

Table 8.2.1: Batteries

Battery Voltage (V) 1 2 3 1+2 1+2+3

Table 8.2.2: Measurements for light bulbs in series.

# of bulbs Battery voltage (V) Current into battery (A) Brightness of bulbs 1 2 3

8.2 Mesaurements

Go to the PHeT web site and use the Circuit Construction Kit simulation (http://phet.colorado. edu/en/simulation/circuit-construction-kit-dc). Drag out three batteries. Q37: Measure the voltage of each using the voltmeter and record the voltage in a Table 8.2.1 and 8.2.2. Then move the batteries end to end as Fig. 8.1.1 to measure combined voltage. Optional fun experiment: take one or two lemons (potatoes, fruit), a penny, and a paper clip. Stick the penny into the lemon next to a paper clip and measure the voltage across it. Try to wire two lemons in series and measure again the electric potential. What happens?

8.2.1 Observations using voltage

Q38: Use the Circuit Construction Kit simulation to build a circuit with a battery and a light bulb. 1. Draw what your circuit looks like. 2. How does the voltage of the battery compare to the light bulb voltage? Explain what you

think is happening. 3. Vary the voltage of the battery and write observations about how the brightness is affected by

voltage. 4. Think about a real light bulb and battery; explain what you think is happening that causes the

changes in brightness.

8.2.2 Observations using voltage in series circuits

Q39: Use Circuit Construction Kit simulation to build the circuits below with a battery at about 12 V and light bulbs. Turn on the voltmeter and ammeter to measure voltage of the battery and current into it. Record bulb brightness with descriptive language.

1. Q40: Summarize the relationships you observed and explain what you think is happening. 2. Test to see if changing the battery voltage causes you to modify any of your conclusions.

Explain what you measured and any conclusions you draw from your tests. 3. Q41: What happens when you take a wire out of a circuit? Explain what you think is

happening 4. Test using the voltmeter or ammeter in different ways. For example: Does it matter if you

take the reading on the left or right of the battery? Switch the meter ends? Describe your tests and results.

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50 Chapter 8. Activity 18: Light Bulbs

Figure 8.2.1: Light bulbs arranged in series.

Table 8.2.3: Measurements for light bulbs in parallel.

# of bulbs Battery voltage (V) Current into battery (A) Brightness of bulbs 1 2 3

8.2.3 Observations using voltage in parallel circuits

Q42: Redo the previous part, but use Fig. 8.2.2 for the circuits. Make a new table and answer the questions.

Figure 8.2.2: Light bulbs arranged in series.

1. Explain what might be happening to cause the change in current. 2. How are current and battery voltage related? What is the shape of the graph? 3. Describe how you could use the simulation to verify the relationship. Test your ideas and

make modifications to your original answers if necessary. Be sure to explain your reasoning.

8.3 Evaluation

Q43: Build the circuit in Fig. 8.3.1. Vary the value of resistor at least ten times. Record in a data table: resistance, current and voltage for each trial.

1. Chart and determine the algebraic relationship for resistance and current. 2. Chart and determine the algebraic relationship for resistance and voltage. 3. Explain the relationships in terms what you think is happening in the circuit. Include how

this experiment is like the one where you added light bulbs.

8.3 Evaluation 51

Figure 8.3.1: Simple circuit with ammeter and voltmeter connected. The ammeter interrupts the current in the battery-resistor circuit. The voltmeter - in contrast - measures the electric potential across the resistor. If the voltmeter were connected in lieu of the ammeter, it would record 0 V, and if the ammeter were connected in lieu of the voltmeter, it would record a large current as it is shorting the circuit.

9. Activity 19: RC Circuits

In this activity, you explore RC circuits. The voltage and current vary as a function of time. The sim- ulation is available at http://phet.colorado.edu/en/simulation/circuit-construction- kit-ac Use this simulation to observe changes that occur in a circuit as time passes. • Observe changes in the current during charging and discharging. • Observe changes in the voltage across a resistor during charging and discharging. • Observe changes in the voltage across a capacitor during charging and discharging.

9.1 Background

For an ohmic resistor the electric potential drop across the resistor is ∆V = IR, where R is the resistance of the resistor and I is the current running through the resistor. The battery creates an electric potential difference, which is ∆V = em f and corresponds to the so called electro-motif force. Finally, a capacitor is made of two oppositely charged plates, the electric field between the plates is uniform and can store energy. The electric potential difference of a capacitor is ∆V = Q/C, where C is the capacitance measured in units of Farad, and Q is the charge on one of the plates (the other plate has the opposite charge; i.e. −Q). Using energy conservation, we know that in a circuit, the sum of the electric potential has to be 0; therefore, we can compute the current I(t) as a function of time t, considering the I = dQ/dt, after solving the first-order differential equation.

9.2 Predictions

Q44: Draw a circuit with a resistor and a capacitor and a battery. Choose practical values for the voltage of the battery, the resistance and the capacitance, such that if the resistor were a light bulb, you would see how the brightness changes over the course of several seconds. Q45: Predict how the current through the resistor changes as a function of time, as you first connect the battery to the capacitor. Q46: Make a design for a circuit that includes switches, such that by opening and closing the switches you can either charge up the capacitor or discharge it.

http://phet.colorado.edu/en/simulation/circuit-construction-kit-ac
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54 Chapter 9. Activity 19: RC Circuits

Resistor Voltage

R

Capacitor Voltage

C

Table 9.3.1: Plot the voltage versus time for the resistor and the capacitor separately, label the axes in each box.

Q47: Predict the voltage across the capacitor as you discharge it as a function of time.

9.3 Measurements

Q48: Take a screenshot after the following procedure and questions for this activity: 1. Access the PhET web site. 2. Click on Simulations. 3. From the left hand menu pick Electricity, Magnets, and Circuits. 4. Choose Circuit Construction Kit: DC & AC (Direct Current & Alternating Current) 5. Create a circuit. It should look similar to Fig. 9.3.1. You may have to replace the red and

black voltmeter connections to the proper location in the circuit.

Figure 9.3.1: RC simulation 1 circuit

1. Charge the capacitor by closing the switch on the left. Sketch the graphs of Voltage vs. Time for the resistor and the capacitor in Table 9.3.1.

2. What happens to the current through the circuit as time goes on? 3. What happens to the amount of charge on the capacitor as time goes on? 4. Now discharge the capacitor by opening the switch on the left and closing the switch on the

right. Sketch the graphs of Voltage vs. Time for the resistor and the capacitor in Fig. 9.3.2. 5. What happens to the current through the circuit as time goes on? 6. What happens to the amount of charge on the capacitor as time goes on?

9.3 Measurements 55

Resistor Voltage

R

Capacitor Voltage

C

Table 9.3.2: Plot the voltage versus time for the resistor and the capacitor separately as they are discharging. Label the axes in each box.

Resistor Voltage

R

Capacitor Voltage

C

Table 9.3.3: Plot the voltage versus time for the resistor and the capacitor. Label the axes in each box.

7. Predict the changes to the graphs if the amount of resistance increases by drawing additional lines on your graphs above. Explain the reasons for your predictions.

8. Right click on the resistor and increase the resistance. Use another color to show the results on your charging and discharging graphs above.

9. Predict the changes to the graphs if the amount of capacitance increases. Use the graphs in Fig. 9.3.3 to show the original graphs and the changes that you predict. Explain the reasons for your predictions.

10. Right click on the capacitor and increase the capacitance. Use another color to show the results on your charging and discharging graphs above.

11. What happens to the current through the circuit as time goes on? 12. What happens to the amount of charge on the capacitor as time goes on? 13. What is the function of a resistor in a circuit? How does it affect the amount of charge that

flows? How does it affect the rate at which charge flows? How does it affect the initial and final voltage across the capacitor?

56 Chapter 9. Activity 19: RC Circuits

9.4 PhET Simulation

Q49: How does placing more than one capacitor affect voltage drops and charge stored in a circuit? Close the left hand switch to charge the capacitors. Q50: How does the voltage drop across each capacitor compare?

Q51: Check the value of the batteries voltage by right clicking on it. How does the voltage drop across each capacitor compare to the voltage across the battery?

Q52: Discharge the capacitors by opening the left switch and closing the right switch. Increase the capacitance of the top capacitor. Repeat the charging process. How does the voltage drop across each capacitor compare?

Q53: What is the relationship between the size of the capacitor and the share of voltage it receives?

Does it appear that placing two capacitors in a circuit with one pathway (series circuit) for charge increases or decreases the amount of charge stored? You may need to return to the original circuit from part I to decide. Q54: Close the bottom switch to charge the capacitors. How does the voltage drop across each capacitor compare?

Figure 9.4.1: RC circuit 2

9.4 PhET Simulation 57

Check the value of the batteries voltage by right clicking on it. How does the voltage drop across each capacitor compare to the voltage across the battery? Discharge the capacitors by opening the bottom switch and closing the top switch. Increase the capacitance of the top capacitor. Repeat the charging process. How does the voltage drop across each capacitor compare? What is the relationship between the size of the capacitor and the share of voltage it receives? What is the relationship between the size of the capacitor and the amount of charge it stores? Does it appear that placing two capacitors in a circuit with multiple pathways (parallel circuit) for charge increases or decreases the amount of charge stored? You may need to return to the original circuit from part I to decide.

Figure 9.4.2: RC circuit 3

10. Activity 20: Series and Parallel Resistors

The simulation is available at http://phet.colorado.edu/en/simulation/circuit-construction- kit-dc-virtual-lab Construct each of the circuits shown in Figs. 10.1.1,10.2.1, and 10.3.1 using the PhET Circuit Simulation. Each light bulb/resistor is 10 Ω by default. The battery has a potential difference of 9 V by default.

10.1 Series Circuit in a Parallel Circuit

1. Q55: On a separate sheet of paper, draw a schematic version of this circuit (replacing bulbs with resistors) and then draw simplified versions to solve.

2. Explain which part of the circuit is in series. Explain which part of the circuit is in parallel. 3. Compare the current in the top branch to the current in the middle branch. Explain why. 4. Q56: Rank the light bulbs in order of brightness. In terms of current flow and resistance,

explain why. 5. Q57: If bulb R2 were removed (right-click to remove), explain what happens to the other

two bulbs and why. 6. Determine which bulbs are affected by each of the switches (S1, S2, S3). Explain why.

Table 10.1.1: Resistance R, electric potential ∆V , current I, and power P for the circuit elements in Fig. 10.1.1.

R ∆V I P 1 2 3 23 battery

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60 Chapter 10. Activity 20: Series and Parallel Resistors

Figure 10.1.1: Circuit with switch, battery, and three light bulbs.

Table 10.1.2: Resistance R, electric potential ∆V , current I, and power P for the circuit elements in Fig. 10.2.1.

R ∆V I P 1 3 battery

10.2 Parallel Circuit in a Series Circuit 1. Q58: On a separate sheet of paper, draw a schematic version of this circuit (replacing bulbs

with resistors) and then draw simplified versions to solve. 2. Explain which part of the circuit is in series. Explain which part of the circuit is in parallel. 3. Q59: Rank the light bulbs in order of brightness. In terms of current flow and resistance,

explain why. 4. Q60: Compare the potential difference across R3 to the potential difference across the other

two bulbs. Explain why. 5. Q61: If R3 were removed (right-click to remove), explain what happens to the other two

bulbs and why. 6. If R2 were removed, what kind of circuit does this become? 7. After R2 is removed, determine what happens to the brightness of each bulb and explain why.

(Hint: Complete the chart if you get stuck.

10.3 Series Circuit in a Parallel Circuit in a Series Circuit 1. Q62: On a separate sheet of paper, draw a schematic version of this circuit ( and ) and then

draw simplified versions to solve. 2. Explain which parts of the circuit are in series. Explain which part of the circuit is in parallel. 3. Q63: Rank the light bulbs in order of brightness. In terms of current flow and resistance,

explain why.

10.3 Series Circuit in a Parallel Circuit in a Series Circuit 61

Figure 10.2.1: Circuit with switch, battery, and three light bulbs.

Table 10.3.1: Resistance R, electric potential ∆V , current I, and power P for the circuit elements in Fig. 10.3.1.

R ∆V I P 1 2 3 4 23 123 battery

Figure 10.3.1: Circuit with switch, battery, and four light bulbs.

11. Activity 22: Faraday’s Law

The simulation is available at http://phet.colorado.edu/en/simulation/faraday. In this activity, you will interact with simulated magnets, compasses, and coils and observe the magnetic fields generated.

11.1 Background

When Hans Christian Ørsted discovered that electricity could be used to produce magnetism, the scientific community anticipated that it would not be long before someone would discover how magnetism could be used to produce electricity. But more than ten years would pass before Michael Faraday solved the puzzle. The application of engineering to electromagnetism led to motors and generators. Nearly any electrical device that produces motion uses a motor. Any device that is plugged into a wall outlet draws power from a generator. Our reliance on applications of electromagnetism is never more apparent than during a power outage. The interactions between electricity and magnetism are not always easy to grasp. In this activity, you will manipulate elements in a simulated laboratory and get visual feedback.

11.2 Bar Magnet

In the first activity, learn about a permanent magnet in the form of a bar magnet. 1. Q64: Run the PhET sim, "Faraday’s Electromagnetic Lab." It should open to the Bar

Magnet tab. Maximize the window. You should see a bar magnet, a compass, and a compass needle grid.

2. Center the bar magnet horizontally on the fourth or fifth row from the top. Set the large compass just below the bar magnet at its midpoint.

3. If the compass needles (in the grid or in the large compass) are to be thought of as arrows indicating the direction of the bar magnet’s magnetic field, each one should be visualized as pointing "north-ward" or "south-ward"

Using the on-screen slider in the control panel, run the strength of the bar magnet up and down. How does the sim show the difference between a strong magnet and a weak magnet?

http://phet.colorado.edu/en/simulation/faraday
64 Chapter 11. Activity 22: Faraday’s Law

Q65: How does the strength of the magnetic field change with increasing distance from the bar magnet and how does the sim show this?

Q66: With the magnet at its strongest, reverse its polarity using the on-screen "Flip Polarity" button in the control panel. What are the ways in which the sim reflects this polarity reversal?

Q67: Describe the behavior of the compass during a polarity reversal (magnet initially at 100%) a. when the compass is touching the bar magnet at its midpoint.

b. when the compass is far from the bar magnet (touching the bottom of the sim window), but still on a perpendicular bisector of the bar magnet,

when the compass is far from the bar magnet and the magnet’s strength is set to 10%.

a. Around the exterior of the bar magnet, the direction of the magnetic field is from its pole to its pole. b. What is the direction of the magnetic field in the interior of the bar magnet? And how did you find out?

Figure 11.2.1: PhET simulation shows compass above a bar magnet. The compass can be moved to detect the magnet field line.

11.3 Electromagnet 65

11.3 Electromagnet

• Step 1: Run the PhET simulation and arrange the on-screen elements so that the top of the battery is along the second or third row of the compass grid. Notice that the magnetic field around the coil is very similar to the magnetic field around the bar magnet. • Step 2: There is no "Strength %" slider on the control panel.

Q68: a. How can you change the strength of the electromagnet?

b. In real life, is it easier to change the strength of a bar magnet or an electromagnet?

• Step 3: There is no "Flip Polarity" button on the control panel. How can you reverse the polarity of the electromagnet?

• Step 4: In the control panel, switch the Current Source from the battery (DC: direct current) to an oscillator (AC: alternating current). If necessary, move the electromagnet so that you can see the entire oscillator. a. What does the vertical slider on the AC source do?

b. What does the horizontal slider on the AC source do?

• Q69: 5: What should the sliders be set to in order to create a "dance party" display? Can you make the dance party even more annoying using the Options menu? Describe.

11.4 Pickup Coil

• Step 1: Run the PhET simulation. You should see a bar magnet, a compass needle grid, and a coil attached to a light bulb. • Step 2: Describe the most effective way of using the magnet and the coil to light the bulb if a.

the coil cannot be moved.

b. the magnet cannot be moved.

66 Chapter 11. Activity 22: Faraday’s Law

• Q70: Step 3: Rank the arrangements in Fig. 11.4.1 and motions shown below from most effective to least effective in terms of lighting the bulb, allowing for ties. For example, if A were most effective, B were least effective, and C and D were equivalent to one another, the ranking would be A > C = D > B.

Figure 11.4.1: Different ways of emf induction using a coil and a permanent magnet bar.

• Step 4: Move the bar magnet through the coil and observe the motion of the electrons in the forward arc of the coil loops. Report the correlations of magnet motion and electron motion.

Figure 11.4.2: Magnet bar configuration.

a. Magnet approaches from the left, north pole first; electrons move downward. b. Magnet departs to the right, south end last; electrons move upward.

Figure 11.4.3: Magnet bar configuration.

c. Magnet approaches from the right, south pole first; electrons move? which, describe! d. Magnet departs to the left, north end last; electrons move? which, describe! e. Magnet approaches from the left, south pole first; electrons move? which, describe! f. Magnet departs to the right, north end last; electrons move? which, describe! g. Magnet approaches from the right, north pole first; electrons move? which, describe! h. Magnet departs to the left, south end last; electrons move? which, describe!

11.5 Transformer 1. Run the PhET simulation and click on the Transformer tab. You should see an electromagnet

and a pickup coil. 2. Q71: Experiment with the various control panel settings and the positions of the electro-

magnet and the pickup coil to determine a method for getting the most light out of the bulb. Describe the settings and locations.

11.6 Generator 67

Figure 11.4.4: Magnet bar configuration.

Figure 11.4.5: Magnet bar configuration.

11.6 Generator 1. Run the PhET simulation and click the on-screen Generator tab. You should see a faucet,

paddle wheel with bar magnet, compass, and a pickup coil. 2. Q72: Experiment with the various settings to determine a method for getting the most light

out of the bulb. Describe the settings.

Q73: What is the story of light production here? Organize and connect the given "elements" and add any key elements that were omitted from the list to construct the complete story. • light radiated from the bulb • changing magnetic field • induced electric current • motion of the bar magnet • kinetic energy of the water • heat the filament

12. Activity 23: Radio Waves

For this acitvity use the Radio Waves & Electromagnetic Fields simulation to guide your under- standing of how Radio broadcasting and Radio receivers work. This simulation is available at http://phet.colorado.edu/en/simulation/radio-waves.

12.1 Prediction

1. Q74: How is the radiating electric field (or electromagnetic signal) produced when radio stations broadcast? Include a description of what is producing the signal as well as the reasoning behind how this could produce a signal.

2. Q75: How does your antenna work to detect this electromagnetic signal produced when radio stations broadcast? Include the physics principles that support your description of how this signal is detected.

12.2 Simulation

Using the simulation, adjust the transmitter so that it is in sinusoidal mode and the electrons are oscillating up and down at a regular frequency. This is how radio waves are broadcast. Set it so that both "display the curve" and the "radiated field" boxes are checked. Q76: What does the curve represent? • The line of electrons being sprayed off of the antenna that then cause the receiver electron to

move. • The path that an electron will follow due to the electromagnetic wave. • The evenly spaced electrons moving up and down between the two antennae. • The field of negative charges that are moving through space. • The strength and direction of the force that would be exerted by the electromagnetic wave on

an electron. With the frequency set at the mid-point of the slider and the amplitude set at the mid-point of the slider, approximately how many grid marks is the wavelength of the wave (use the pause button

http://phet.colorado.edu/en/simulation/radio-waves
70 Chapter 12. Activity 23: Radio Waves

and step button as you need to in order to get a good measure, and round to the nearest whole grid mark)? Q77: If the amplitude is increased, the wavelength • decreases • increases • stays the same

Q78: Use the simulation to evaluate the following statements. TRUE FALSE If the oscillation frequency of the transmitting electron decreases,

the oscillation frequency of the electron in the receiver is instantaneously affected. TRUE FALSE The electron in the receiving antenna oscillates at a lower frequency

than the electron in the transmitting antenna because of the distance between the antennas. TRUE FALSE If the frequency of oscillation increases but the amplitude of the

electron oscillation remains the same, then the electron in the transmitting antenna is experiencing larger accelerations (recall what you know about acceleration and motion).

TRUE FALSE If the amplitude increases but frequency remains the same, the electron at the receiving antenna experiences larger peak forces but oscillates at the same frequency as before.

TRUE FALSE If the frequency of the transmitting electron decreases by a factor of two, it will now take longer for the electromagnetic signal to reach the receiving antenna.

TRUE FALSE If the frequency decreases, the wavelength decreases. TRUE FALSE The electromagnetic waves generated by the transmitting antenna

produce currents in the receiving antenna. TRUE FALSE When the electron in the transmitting antenna is at its peak height,

the electron in the receiving antenna is always also at its peak height. Explain your reasoning to your answer for the T/F If the frequency of oscillation increases but the amplitude of the electron oscillation remains the same, then the electron in the transmitting antenna is experiencing larger accelerations (recall what you know about acceleration and motion). Include in your explanation how this affects the strength of the transmitted electromagnetic signal (revisit the simulation if you did not notice what happened to the strength of the transmitted signal). Q79: For the radio wave transmitter in the simulation, which of the following orientations of the receiver antenna will pick up the signal? (Select all that will) • an antenna oriented vertically • an antenna oriented horizontally (parallel to the ground) with one tip pointing towards the

transmitting antenna (so it is oriented East-West) • an antenna oriented horizontally and perpendicular to the antenna in the previous answer (so

it is oriented North-South) Q80: Which one of the sets of graphs in Fig. 12.2.1 and 12.2.2 corresponds with the motion of the electron in the receiving antenna? (It may help to remember the relationship between force and acceleration, and use the "Step" feature to step through the motion of the electron and have the vectors display the ?force on an electron?.) Which is the correct graph from Figs. 12.2.1 and 12.2.2?

12.2 Simulation 71

Figure 12.2.1: Position versus time, speed versus time, and acceleration versus time for radio signals.

Figure 12.2.2: Position versus time, speed versus time, and acceleration versus time for radio signals.

II 13 Lab 1: Measuring Charges . . . . . . . . . . . 75 13.1 Tools 13.2 Prediction 13.3 Experiment 13.4 Evaluation

14 Lab 2: Magnetic Fields . . . . . . . . . . . . . . . 77 14.1 Tools 14.2 Prediction 14.3 Experiment 14.4 Evaluation

15 Lab 3: Arduino Battery Test . . . . . . . . . . . 79 15.1 Tools 15.2 Prediction 15.3 Experiment 15.4 Evaluation

16 Lab 4: Resistor Circuits . . . . . . . . . . . . . . . 83 16.1 Tools 16.2 Prediction 16.3 Experiment 16.4 Evaluation

17 Lab 5: Voltage Divider . . . . . . . . . . . . . . . 85 17.1 Tools 17.2 Prediction 17.3 Experiment 17.4 Evaluation

18 Lab 6: RC circuit . . . . . . . . . . . . . . . . . . . . . 87 18.1 Tools 18.2 Prediction 18.3 Experiment 18.4 Evaluation

Hands-on Experiments

13. Lab 1: Measuring Charges

In this lab, you will measure quantitatively the number of electrons that you can remove from an insulator.

13.1 Tools

For this lab, you will need the following: • Tape, Straws, Balloons, or similar insulators • Ruler

13.2 Prediction

Please read the lab guidelines in section 2 (page 13) carefully before starting the experiment. For this experiment, you will need to be familiar with Chapter 14 in Matter and Interactions.[2] In Paragraph 14.2, you can read how you can charge certain objects. It is noteworthy that only insulators can be easily charged. Note that dry hands, gloves, and so on will also help isolating the device, when you do the experiment. In the textbook, the paragraph "How much charge is on a charged object?" will help you come up with an equation for the amount of charge Q that you remove from an object by watching the attraction. You need to realize that all objects (including yourself) are based on atoms. Atoms contain electrons. If one of the outer electrons is missing, the object becomes charged. For insulators, electrons can be removed using friction (rubbing a drinking straw with another insulator). The charged object and a neutral object interact electrostatically. You should be able to show that based on information of Coulomb’s law. Q81: What are the units for charge? Q82: Choose two light objects, which can move, such as two straws stuck on a nail that can rotate, two pieces of tape one held by two bookends, . . . , be creative. Q83: Draw a force diagram that shows all the forces on the charged object. In the balance of the electrostatic force (Coulomb’s force) and the gravitational force, then use the momentum principle and write out the equation using the parameters that you have put in the diagram.

76 Chapter 13. Lab 1: Measuring Charges

Q84: Write an expression, by solving the momentum principle, that shows how the charge Q on the charged object is related to the the separation distance d. Q85: Predict a typical number of electrons that you would expect can be removed from an insulator. Put this number in perspective; i.e. compare to something else that has a similar number. Q86: How could you compute the mass m of a small object without using a scale?

13.3 Experiment Perform the experiment and record all details in your bound lab notebook. Make a table with several rows, one for each trial. Add columns where you record the precise distance (see Section 2.5 on page 15), finally add a column with the charge Q that you deduce for the model developed in the prediction. Hint: You can find some guidance in the "Experiments" section at the end of Chapter 14.[2] However, try out several approaches, before you start recording systematic results for the experiment. Explore different options. If something does not work try to solve the problems (sometimes by getting help, ideas from peers). For example, if the room is too humid, then it will be much harder to insulate charges, a dry environment will be useful. Handling the insulators with gloves may provide additional insulation, using silk or fur to remove charges is most useful. Q87: Include a photo from the experiment that shows your name and the date of the experiment, see for an example Fig. 2.2.1 on page 15.

13.4 Evaluation Q88: Compute the amount of charge for each measurement (you should have at least 5 measure- ments). Q89: Make a graph that plots Q(d), the charge Q as a function of the separation distance d for a given mass m. On the graph, also plot the points from your experiment. Use lines for the models and points for the data points that you experimentally measure. Q90: How does the number of electrons from the prediction compare the measured number, and how does it compare to numbers from the book and literature? Does your answer make sense? Q91: What did you learn in this experiment? Q92: What aspect of the experiment is not clear to you yet?

14. Lab 2: Magnetic Fields

Magnetic fields can be measured using a compass. With this experiment, you will learn how to measure the magnetic moment of any permanent magnet using a compass.

14.1 Tools

For this lab, you will need the following: • compass (phone may work) • strong magnet • ruler

If you are using the iPad, phone, or similar device as an electronic compass, then it is good to familiarize yourself where the "compass" is located. Generally in iPhone (depending on the series) in the top right there is a magnetoresistive device from permalloy (alloy of nickel and iron, which is magnetically soft). The resistance in such a device depends on the direction of the magnetization with the current. If the current direction is known, then the magnetic direction is obtained. Using the information of the Earth’s magnetic field, the direction information can then be used to determine the magnitude of the magnetic field. There are apps that will do the math, but for the purpose of this lab you should just read the angle of the magnetic field and deduce the magnitude using the concept of superposition of magnetic fields. It is noteworthy that the iPhone’s compass, for example, may lag, so moving the magnet very slowly, and then holding it in position will be useful. Make sure to record the position with respect to the position of the magnetoresistive device that is used to measure the magnetic direction. You will need to practice for a good while. The use of a regular compass in this situation may simplify matters. The use of a compass is more straightforward. Please note that a magnet that points to the magnetic north pole is a south pole, as opposites attract.

14.2 Prediction

Please read the lab guidelines in section 2 (page 13) carefully before starting the experiment.

78 Chapter 14. Lab 2: Magnetic Fields

Certain materials are permanent magnets, such as iron, nickel, cobalt, and their alloys. That means, even in the absence of an applied magnetic field, they have a magnetization due to Weiss domains that form from interactions between the magnetic spins of unpaired electrons. Magnets have poles, generally denoted as North and South poles. Opposite poles attract each other. Q93: For a permanent bar magnet, how does the magnetic field |~B| depend on the distance r? Make a plot of what the field strength dependence is on distance. Q94: Find the magnetic declination for your area using http://www.ngdc.noaa.gov/geomag- web/#igrfgrid or a similar website. The declination is the deviation of the compass North direction and the direction of the North pole defined by the rotating axis. Also find the strength of the magnetic field for your location. (This information will not be used in the following calculations but it is interesting to know and adds to our understanding.) Q95: According to Chapter 17, "Detecting Magnetic Fields", it is possible to determine the magnetic field strength from the angle of the compass needle. Make a diagram of the compass, a permanent magnet, and the Earth’s magnetic field. Define the angles in the diagram and re-derive the equation for the magnetic field strength based on the angle of the compass. It should be an equation of B(θ) = . . . , where θ is the angle that you define in your diagram.

14.3 Experiment Place the magnet next to the ruler and use the compass to measure the angle as a function of the distance from the permanent magnet. Make a table and list at the minimum 10 measurements. Adjust the magnet and distances, so that you get measurable changes in the angle as you adjust the distance between the compass and the permanent magnet. Note that in that region of distance the magnetic field of the Earth and the magnetic field of the permanent magnet are similar. Add an extra column to the table and compute the magnetic field strength |~B| for each given angle. Verify that the field data makes sense. Q96: Make a graph of the data points with the distance d along the x-axis and the magnitude of the magnetic field B along the y-axis. Q97: Determine the effective magnetic dipole moment of the permanent magnet that you have measured. Q98: Include a photo from the experiment that shows your name and the date of the experiment, see for an example Fig. 2.2.1 on page 15.

14.4 Evaluation Q99: Compare the magnetic dipole moment with the values provided in the book. Is it larger or smaller? Why do you think? Q100: Does the magnet really behave like a dipole? Can you measure the exponent of how the field decays with distance? Hint: If you have an equation, such as B(r) = A/rn, where r is the separation distance between observer and source, and A is some constant, and B is the magnetic field, then you can experimentally fit the exponent n by using the following schema that scientists and engineers often use. First realize, that you can rewrite the equation as B(r) = Ar−n. Now, rewrite it as B(r)/A = r−n. Take the natural log of this equation and you get ln(B/A) =−n lnr. Imagine that define new variables y≡ ln(B/A) and x≡ lnr, then you have y =−nx. You realize that −n is the slope. In summary, if you are able to plot your measurement variables B and r on a log-log plot, then you will observe a linear behavior where the slope is equivalent to n, the exponent. The mathematically keen observer will note that the offset is equivalent to lnA, since ln(B/A) = ln(B)− ln(A).

http://www.ngdc.noaa.gov/geomag-web/#igrfgrid
http://www.ngdc.noaa.gov/geomag-web/#igrfgrid
15. Lab 3: Arduino Battery Test

In this lab, you will get familiar with the Arduino micro-controller, see section 1.2.1. The objective is to learn about the electric potential, measuring voltages, and batteries.

15.1 Tools

For this lab, you will need the following: • Arduino (see section 2.8) • breadboard (see section 2.8.1) • Wires • Computer / laptop with Arduino software installed • 2 kΩ resistor • used and new batteries

Remember that you can make a 2 kΩ resistor by adding two 1 kΩ resistors in series, or by using five 10 kΩ resistors in parallel. There are other configurations as well. The exact amount of the resistor is not important, however, the order of magnitude is important, so that the current to the Arduino board is limited. Note that according to Ohm’s law, lower resistance would imply more current from the battery.

15.2 Prediction

Please read the lab guidelines in section 2 (page 13) carefully before starting the experiment. Q101: What is the current running through the wire, if you connect a 2 kΩ resistor with 1.5 V battery. What is the current, if you connect it to a 3 V battery, or a 4.5 V battery instead. Fill out table 15.2.1. Q102: Draw a circuit, with the battery connected to the resistor, the resistor connected to the analog input port A0. The battery also needs to be connected to the ground (GND) on the Arduino board. Q103: The Arduino has a 10-bit DAC converter. It takes the analog signal (voltage) and converts it into digital format. It cannot do this conversion with infinite precision, rather it uses 10-bits,

80 Chapter 15. Lab 3: Arduino Battery Test

Table 15.2.1: Assuming that you have a 2 kΩ resistor as the load for the battery, find the current in the proper units.

Battery Current (V) (mA) 1.5 3.0 4.5

which means 210 possible voltage states. What is the smallest voltage it can distinguish, if the maximum voltage is 5 V? Q104: What difference do you expect in voltage do you expect from measuring a new battery and a used battery?

15.3 Experiment

15.3.1 First Arduino Program

If this is the first time that you are using the Arduino board, make sure to read how to connect it to the computer and verify that your board is working properly by running the LED blink code in Listing 15.1. For this code, you connect an LED to pin 13, note the polarity of the LED. The long pin is to be connected to pin 13 and the short pin to the ground (GND). Importantly, a red LED will get busted if you apply 5 V, so in general you have to lower the voltage to ≈ 2 V using a voltage divider, see chapter 17. However, pin 13 for most boards is special in that it has a resistor and sometimes an LED already on the board, therefore connecting an LED is safe. Otherwise, you would have to use a resistor in series with the LED in order to limit the current and divide the voltage.

Listing 15.1: Arduino code to make an LED connected to pin 12 blink. The short leg of the LED needs to be connected to a resistor, which is connected to the ground.

1 vo id s e t u p ( ) { / / d e f i n e whe ther p i n 13 i s an i n p u t or an o u t p u t pinMode ( 1 3 , OUTPUT ) ;

}

6 vo id loop ( ) { / / t u r n on t h e LED d i g i t a l W r i t e ( 1 3 , HIGH ) ; d e l a y ( 5 0 0 ) ; / / w a i t 0 . 5 s / / t u r n o f f t h e LED

11 d i g i t a l W r i t e ( 1 3 , LOW) ;

/ / w a i t f o r 1000 ms d e l a y ( 1 0 0 0 ) ;

}

15.3.2 Testing Batteries

Make a table with a row for each battery and a column for voltage. Determine the average voltage of used batteries and the average voltage of new batteries. Make several measurements and then

15.4 Evaluation 81

take the average and find the standard deviation. Determine the difference in voltage of an empty battery and a new battery. The voltage of the battery can be measured with the code from Listing 15.2. It assumes that you connect the positive end of the battery to the A0 port. Use the serial monitor to read the voltage values; it should be printed in units of volts. Add two batteries and three batteries in series and again measure the voltage. What happens to the electric potential? Be careful, when connecting the batteries in series, in particular, observe the polarities. As a safety note, if you short the batteries a large current can flow, avoid this by always using a resistor as a load. Note any details that you observe during your procedure. Those notes will be useful in the lab report. Q105: Include a photo from the experiment that shows your name and the date of the experiment, see for an example Fig. 2.2.1 on page 15.

Listing 15.2: Arduino code to measure voltage from input A0.

/ / d e f i n e g l o b a l v a r i a b l e s i n t a n a l o g V a l u e = 0 ; f l o a t v o l t a g e = 0 ;

5 vo id s e t u p ( ) {

/ / needed f o r s e r i a l o u t p u t S e r i a l . b e g i n ( 9 6 0 0 ) ;

} 10 vo id loop ( )

{ / / read A0 a n a l o g V a l u e = ana logRead ( 0 ) ; / / c o n v e r t v a l u e t o v o l t a g e

15 v o l t a g e = a n a l o g V a l u e ∗ 5 . 0 / 1024 ; S e r i a l . p r i n t l n ( v o l t a g e ) ;

/ / w a i t f o r 1000 ms d e l a y ( 1 0 0 0 ) ;

20 }

15.4 Evaluation Q106: What is the difference between AA, and AAA, or C batteries, or lithium batteries, when measuring the electric potential? Q107: What did you learn in this experiment? What surprised you?

16. Lab 4: Resistor Circuits

In this lab, you will understand resistors and series and in parallel. This hands-on experiment gives you experience in setting up resistors in parallel and series and make measurements of electric potential differences.

16.1 Tools

For this lab, you will need the following: • Arduino (see section 2.8) • several resistors and wires • breadboard (see section 2.8.1)

16.2 Prediction

Please read the lab guidelines in section 2 (page 13) carefully before starting the experiment. Q108: Draw a circuit with 3 resistors in parallel (circuit 1) and another circuit with 3 resistors in series (circuit 2) Q109: Build a new circuit, which has at least two resistors in series and at least two resistors in parallel (circuit 3). It is a mixed circuit. Label all the resistors individually, assign currents, and use the Node Rule and Loop Rule to solve for the electric potential in each of the resistors. Fill out a table similar to Table 16.2.1 with your results. Be creative with the circuit.

Table 16.2.1: Three circuits with resistors and the electric potential difference across the resistor. The battery provides an emf of 5 V.

Circuit R1 ∆V1 R2 ∆V2 R3 ∆V3 R4 ∆V4 1 (parallel) 2 (series) 3 (mixed)

84 Chapter 16. Lab 4: Resistor Circuits

16.3 Experiment Build at least 3 circuits (see predictions) and measure the voltage across each resistor using the Arduino. Then compare with the predictions. You can use the code from Listing 15.2 to measure the voltage across a resistor. Note that you may have to move the wire to different resistors in order to make the measurements. Make a schematic drawing of each circuit that you build on the breadboard (see section 2.8.1) in your lab notebook. Q110: Make a table similar to one shown as Table 16.2.1; you may add additional columns if you are using more resistors. Q111: Include a photo from the experiment that shows your name and the date of the experiment, see for an example Fig. 2.2.1 on page 15.

16.4 Evaluation It is noteworthy, that the resistor is a linear device (∆V = IR) in the sense that you increase the resistance, the electric potential at fixed current increases. There are many other devices which are linear, for example a spring (|F |=−k∆x), for a fixed displacement ∆x, the force changes linearly. Therefore parallel and serial spring systems can be understood in the same way. In fact, there is a multitude of systems which have such linear relationships and can be combined in series and parallel. Can you think of other systems and do you better understand these systems? Q112: How many significant digits can you include in your results for the voltage measurements? Q113: What did you learn with this experiment?

17. Lab 5: Voltage Divider

In this lab, you will quantify insulators and conductors. After the lab, you will be able to build a voltage divider

17.1 Tools

For this lab, you will need the following: • Arduino • various resistors and wires • several household items for testing (some insulators, some conductors)

17.2 Prediction

Please read the lab guidelines in section 2 (page 13) carefully before starting the experiment. Q114: Make a drawing of a voltage divider. The Arduino microcontroller will provide 5 V and GND. You will use A0 input to measure the voltage. One resistor on the voltage divider is known, the other is not known. Q115: Use proportions and show how the measured voltage is related to the resistance of the unknown part.

17.3 Experiment

Create a table that lists the items in one row. Another column is used for designation of conductors and insulators. The third column should show the voltage measured across the unknown resistor, and the calculated resistance of the unknown device in the forth column. Use the code from Listing 15.2 on page 81. Be creative with the items that you want to test; some common items should include paper clip, Al foil, fruit, dry and wet wood pieces, . . . Q116: Include a photo from the experiment that shows your name and the date of the experiment, see for an example Fig. 2.2.1 on page 15.

86 Chapter 17. Lab 5: Voltage Divider

17.4 Evaluation Q117: Categorize items based on the resistance into two classes of insulators and conductors. Compare the colors of the insulators and conductors. What can you conclude? Q118: Choose one item that and repeat the measurement for different main resistors. You can put two resistors in series to increase the resistance, or put them in parallel to build a new resistor. Then plot the resistance of the unknown device as a function of the resistance of the known resistor, the main resistor.

18. Lab 6: RC circuit

In this lab you will put together RC circuits, where a resistor and capacitor are combined in series. The resulting circuit has a characteristic time τ = RC. If the empty capacitor is charged, then after the time τ , it will have (1− e−1) or roughly 67% of the maximum charge that you can put on that capacitor (which is Qmax =C∆V ).

18.1 Tools

For this lab, you will need the following: • Arduino • resistor and wires • capacitor

18.2 Prediction

Please read the lab guidelines in section 2 (page 13) carefully before starting the experiment. Design an experiment that will measure quantitatively the time-dependence of an RC circuit. Use at least 3 different circuits, vary the resistance or vary the capacitance and make a prediction of the electric voltage across the resistor as a function of time. Measuring the voltage as a function of time, verify the exponential shape and determine the time constant. Make sure that the experimental time constant is in the range of 100 ms to 10 s, such that you have a chance to make a measurement. Q119: What resistors are you using? What capacitances are you using? Build a table similar to Table 18.2.1 that includes the values of the resistances and capacitances and also the time constants. Q120: Make a sketch of the diagram for an RC circuit and how the measurement with the Arduino will be done. Note that the Arduino provides the positive voltage and the ground. It will also read the electric potential at A0 with respect to the ground. Q121: Predict how you would expect the voltage across the resistor to behave as a function of time. Graph time on the x-axis and voltage on the y-axis. Also mark approximate values. What is the maximum voltage and what is the minimum voltage? What are the time steps?

88 Chapter 18. Lab 6: RC circuit

Table 18.2.1: List of resistors R and capacitors C with computed time constant τ . Make sure to include the units in the table.

R C τ 1 2 3

18.3 Experiment

You can compare the results of your experiment with the simulation in PhET using the Circuit Construction Kit at http://phet.colorado.edu/en/simulation/circuit-construction- kit-ac. Think about how you can charge and discharge the capacitor in your circuit. In the simulation, you discharge the capacitor by right-clicking, but how would you do it with the real capacitor. Q122: Build the circuits and measure the electric potential as a function of time. You may be able to copy the output from the Serial monitor directly into a spreadsheet and then use then use the functionality "Data", "Text to Columns" to create two columns off the comma-separated data generated with code in Listing 18.1. Q123: Extract the time constant from the data by fitting or graphing carefully. Q124: Include a photo from the experiment that shows your name and the date of the experiment, see for an example Fig. 2.2.1 on page 15. HELP: Use the Serial Monitor to record the values. You will need to also record the time, which can be done in Arduino language with the command millis(), which returns the time in units of 1/1000 s. A small modification to the previous code from Listing 15.2 on page 81 is made to include the time measurements, see new Listing 18.1 on page 88.