Electric field hockey activity worksheet answers

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

https://arxiv.org/
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