Magnetic field of a solenoid lab answers

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Florida International University

GENERAL PHYSICS

LABORATORY 2

MANUAL Edited Fall 2019

1

Florida International University

Department of Physics

Physics Laboratory Manual for Course

PHY 2049L

Contents

Course Syllabus 2

Grading Rubric 4

Estimation of Uncertainties 5

Vernier Caliper 9

Experiments

1. Electrostatics 10

2. Coulomb's Law 13

3. Electric Field and Potential 16

4. Capacitors 21

5. Ohm's Law and Resistance 27

6. Series and Parallel Circuits 33

7. Magnetic Force on Moving Charges 40

8. Magnetic Field of a Solenoid 44

9. Faraday's Law & Lenz's Law 49

10. Reflection & Refraction 53

11. Mirrors, Lenses, Telescope 57

12. Double-Slit Interference 62

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COURSE SYLLABUS

LAB COORDINATOR

Email: Please use Canvas Inbox

UPDATES

Updates to the lab schedule, make-up policy, etc. may be found on Canvas.

CLASS MEETINGS

• During Fall and Spring Semesters classes start the second week of the semester and end the week prior to the final exam week.

• Students that have missed their own section may attempt to make-up by attending another section during the time the same experiment is conducted (see PantherSoft for

available sections). Admission for make-up is granted by the Instructor on site, no

reservation, no guaranteed seating.

• Students must sign in each class meeting to verify attendance.

ACTIVE LEARNING

One of the important goals of this lab course is to strengthen your understanding of what you

have learned in the classroom. You will be working in groups and encouraged to help each other

by discussing among yourselves any difficulties or misconceptions that occur to you. Apart from

the instructor in charge, student Learning Assistants (LA) will be on hand to encourage

discussion, for example by posing a series of questions.

LAB REPORTS

You will be required to submit a lab report at the end of the class period. The format of the report

is dictated by the experiment. As you work your way through the experiment, following the

procedures in this manual, you will be asked to answer questions, fill in tables of data, sketch

graphs, do straightforward calculations, etc. You should fulfill each of these requirements as you

proceed with the experiment. Any preliminary questions could be answered before coming to the

lab, thereby saving time. This way, you will effectively finish the report as you finish the

experiment. Note that for experiments that require them, blank or partially filled in data tables

are provided on separate perforated pages in this manual at the end of the experiment. You may

carefully tear them out along the perforation and staple them to the rest of your report.

GRADES

• The weekly lab reports and your active participation will determine your grade in the

course. Each week you will receive 30% for active participation and up to 70% for your lab

report.

• A missed assignment or lab will receive a ZERO grade.

• Lab reports are to be handed in before you leave the lab.

• THERE IS NO FINAL EXAM

• The grading system is based on the following scale although your instructor may apply a

"curve" if it is deemed necessary. In addition, “+” and “-“may be assigned in each grade

range when appropriate.

o A: 90-100%

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o B: 75-90% o C: 60-75% o D: 45-60%

WHAT YOU NEED TO PROVIDE

Calculator with trig. and other math functions including mean and standard deviation.

AT THE END OF CLASS.

1. Disconnect all sensors that you have connected. 2. Report any broken or malfunctioning equipment. 3. Arrange equipment tidily on the bench.

DROPPING THE LECTURE BUT NOT THE LAB

If you find it necessary to drop the lecture course, PHY 2049 or PHY 2054, you do not also have

to drop this lab course, PHY 2049L. However, you will need to see a Physics Advisor and get a

waiver.

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GRADING RUBRIC

Expectations for a successfully completed experiment and lab report are indicated in the

following rubric. Note that not every scientific ability in the rubric may be tested in every

experiment. Therefore, the graders will determine the maximum number of points attainable for

an experiment (usually 18) and indicate your score as a fraction, e.g 16/18.

Grade Scientific

ability

Missing

(0 pt)

Inadequate

(1 pt)

Needs

improvement

(2 pt)

Adequate

(3 pt)

Attempt to

answer

Preliminary

Questions

No attempt to

answer

Preliminary

Questions

Answers to

Preliminary

Questions

attempted

Able to draw

graphs/diagrams

No graphs or

drawings

provided

Graphs/drawings

poorly drawn with

missing axis labels

or important

information is

wrong or missing

Graphs/drawings

have no wrong

information but a

small amount of

information is

missing

Graphs/drawings

contain no

omissions and are

clearly presented

Able to present

data and tables

No data or

tables

provided

Not all the relevant

data and tables are

provided

Data and tables are

provided but some

information such as

units is missing

Complete set of

data and tables

with all necessary

information

provided

Able to analyze

data

No data

analysis or

analysis

contains

numerous

errors

Data analysis

contains a number

of errors indicating

substantial lack of

understanding

Data analysis is

mostly correct but

some lack of

understanding is

present

Data analysis is

complete with no

errors

Able to answer

Analysis

questions

No Analysis

questions

answered

Less than half the

questions

unanswered or

answered

incorrectly

Less than a quarter

of the questions

unanswered or

answered

incorrectly

All questions

answered

correctly

Able to conduct

experiment as

evidenced by the

quality of results

Little or no

experimental

ability as

evidenced by

poor quality of

results

Results indicate a

marginal level of

experimental ability

Results indicate a

reasonable level of

experimental

ability with room

for improvement

Results indicate a

proficient level of

experimental

ability

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ESTIMATION OF UNCERTAINTIES

The purpose of this section is to provide you with the rules for determining the uncertainties in

your experimental results. All measurements have some uncertainty in the results due to the fact

you can never do a perfect experiment. We begin with the rules for estimating uncertainties in

individual measurements, and then show how these uncertainties are to be combined to produce

the uncertainty in the final result.

The “absolute uncertainty” in a measured quantity is expressed in the same units as the quantity

itself. For example, length of table = 1.65 ± 0.05 m or, symbolically, L ± L. This means we are

reasonably confident that the length of the table is between 1.60 and 1.70 m, and 1.65 m is our

best estimate. If L is based on a single measurement, it is often a good rule of thumb to make L

equal to half the smallest division on the measuring scale. In the case of a meter rule, this would

be 0.5 mm. Other considerations, such as a rounded edge to the table, may make us wish to

increase L. For example, in the diagram, the end of the table might be estimated to be to be at

35.3 ± 0.1 cm or even 35.3 ± 0.2 cm.

If the same measurement is repeated several times, the average (mean) value is taken as the most

probable value and the “standard deviation” is used as the absolute uncertainty. Therefore, if the

length of the table is measured 3 times giving values of 1.65, 1.60 and 1.85m, the average value

is

The deviations of the 3 values from the average are -0.05, -0.10 and +0.15m, and the standard

deviation

So now we express the length of the table as 1.7 ± 0.1 m.

Note: Your calculator should be capable of providing the mean and standard deviation

automatically. Excel can also be used to calculate these quantities.

165 160 185

3 170

   

+ + = m

= sum of squares of deviations

number of measurements

= + +

= 0 05 010 015

3 01

2 2 2. . . . m

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Generally, it is only necessary to quote an uncertainty to one, or at most two, significant

figures, and the accompanying measurement is rounded off (not truncated) in the same decimal

position.

“Fractional uncertainty” or “percentage uncertainty” is the absolute uncertainty, expressed as a

fraction or percentage of the associated measurement. In the above example, the fractional

uncertainty, L/L is 0.1/1.7 = 0.06, and the percentage uncertainty is 0.06 x 100 = 6%.

Rules for obtaining the uncertainty in a calculated result.

We now need to consider how uncertainties in measured quantities are to be combined to

produce the uncertainty in the final result. There are 2 basic rules:

A) When quantities are added or subtracted, the absolute uncertainty in the result is equal to

the square root of the sum of the squares of the absolute uncertainties in the quantities.

B) When quantities are multiplied or divided, the fractional uncertainty in the result is equal

to the square root of the sum of the squares of the fractional uncertainties in the

quantities.

Examples

1. In calculating a quantity x using the formula x = a + b - c, measurements give

a = 2.1 ± 0.2 kg

b = 1.6 ± 0.1 kg

c = 0.8 ± 0.1 kg

Therefore, x = 2.9 kg

The result is therefore x = 2.9 ± 0.2 kg

2. In calculating a quantity x using the formula x = ab/c, measurements give

a = 0.75 ± 0.01 kg

b = 0.81 ± 0.01 m

c = 0.08 ± 0.02 m

Therefore x = 7.59375 kg (by calculator).

Fractional uncertainty in x,



x

x =

0.01

0.75



 



 

2

+ 0.01

0.81



 



 

2

+ 0.02

0.08



 



 

2

= 0.25

Absolute uncertainty in x, x = 0.25  7.59375

= 2 kg (to one significant figure)

The result is therefore x = 8 ± 2 kg

Note: the value of x has to be rounded in accordance with the value of x. If x had been

calculated to be 0.003 kg, the result would have been x = 7.594 ± 0.003 kg.

3. The following example involves both rule A and rule B.

In calculating a quantity x using the formula x = (a + b)/c, measurements give

Absoluteerror in x x kg, . . . . = + + =0 2 01 01 0 22 2 2

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a = 0.42 ± 0.01 kg

b = 1.63 ± 0.02 kg

c = 0.0043 ± 0.0004 m3

Therefore x = 476.7 kg/m3

Absolute uncertainty in kg 02.002.001.0 22 =+=+ ba

Fractional uncertainty in a + b = 0.02 / 2.05 = 0.01

Fractional uncertainty in c = 0.0004 / 0.0043 = 0.093

Fractional uncertainty in 094.001.0093.0 22 =+=x

Absolute uncertainty in x, x = 0.094 476.7 = 40 kg/m3 (to one significant figure)

The result is therefore x = 480 ± 40 kg/m3

Note that almost all of the uncertainty here is due to the uncertainty in c. One should therefore

concentrate on improving the accuracy with which c is measured in attempting to decrease the

uncertainty.

Uncertainty in the slope of a graph

Often, one of the quantities used in calculating a final result will be the slope of a graph.

Therefore, we need a rule for determining the uncertainty in the slope. Graphing software such as

Excel can do this for you. Another way to do this is “by hand” as follows: In drawing the best

straight line (see figure on following page),

1. The deviations of the data points from the line should be kept to a minimum. 2. The points should be as evenly distributed as possible on either side of the line. 3. To determine the absolute uncertainty in the slope:

a. Draw a rectangle with the sides parallel to and perpendicular to the best straight line that just encloses all of the points.

b. The slopes of the diagonals of the rectangle are measured to give a maximum slope and a minimum slope.

c. The absolute uncertainty in the slope is given by:



max slope - min slope

2 n , where n

is the number of data points.

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What has been described above is known as “standard uncertainty theory”. In this system, a

calculated result, accompanied by its uncertainty (the standard deviation s), has the following

properties: There is a 70% probability that the “true value” lies within the ± s of the calculated

value, a 95% probability that it lies within the ± 2s, a 99.7% probability that it lies within ± 3s,

etc. We may therefore state that the “true value” essentially always lies within plus or minus 3

standard deviations from the calculated value. Bear this in mind when comparing your result

with the expected result (when this is known).

Some final words of warning

It is often thought that the uncertainty in a result can be calculated as just the percentage

difference between the result obtained and the expected (textbook) value. This is incorrect. What

is important is whether the expected value lies within the range defined by your result and

uncertainty.

Uncertainties are also sometimes referred to as “errors.” While this language is common practice

among experienced scientists, it conveys the idea that errors were made. However, a good

scientist is going to correct the known errors before completing an experiment and reporting

results. Erroneous results due to poor execution of an experiment are different than uncertain

results due to limits of experimental techniques.

Fig. 1 Graph of extension vs. mass

Mass (kg)

2 3 4 5 6 7

Exten sion(

mm)

4

6

8

10

12

14 Best line

Min. slope Max. slo

pe

9

VERNIER CALIPER

A Vernier scale allows us to measure lengths to a

higher degree of precision than can be obtained with,

say, a millimeter scale. In Fig. 1, a moveable Vernier

scale V is placed next to a millimeter scale M (e.g. on a

meter rule). V is 9mm long and has 10 divisions, each

of length 0.9 mm, so each division on V is shorter than

each division on M by 0.1 mm Fig. 1

Suppose we wish to measure the position on a

meter rule of the right-hand end of an object. V is

positioned as shown in Fig. 2. Clearly the required

reading is somewhere between 24 and 25 mm. To

obtain the fractional part, we note which graduation

on V lines up (or comes closest to lining up) with a

graduation on M. In Fig. 2 it is the 7th, labeled B,

which lines up with C, and the required reading is

therefore 24.7 mm. The reasoning is as follows: Fig. 2

The graduation on V to the left of B is 0.1 mm to the right of the closest graduation on M. The

graduation on V two to the left of B is 0.2 mm to the right of the closest graduation on M, etc.

Therefore the graduation labeled A will be 0.7 mm to the right of the graduation D on scale M.

A tool to measure linear dimensions is the Vernier caliper shown in Fig. 3. It consists of a scale

M graduated in millimeters and attached to a fixed jaw A, and a Vernier scale V on a moveable

jaw B.

Fig.3

Fig. 3

Note that part of the scale M can be seen through an opening in the moveable jaw. When the

jaws are closed, the zero graduations on M and V coincide. The object, C, to be measured is

placed snugly between the jaws by sliding B. The length can then be read from scales M and V.

In Fig. 3, the reading is 2.57 cm. (By counting backwards from the 3 cm graduation, you can see

that the leftmost graduation on V is between 2.5 and 2.6 cm.)

20 mm 30 mm

V

M

A B

CD

Object

1cm0cm 5cm M

A B

C

3

V

cm

B

30 mm 40 mm

V

M

10

Lab 1. Electrostatics

Electric charge, like mass, is a fundamental property of the particles that make up matter. However, unlike mass, charge comes in two forms that we label positive (e.g. the charge of a proton) and negative (e.g. the charge of an electron). Normal matter is made up of "neutral" atoms having equal numbers of protons and electrons but, for example, can become negatively charged by gaining electrons, or positively charged by losing electrons. Charged objects of the same sign repel each other whereas those of opposite sign attract each other. In the first part of this experiment, an "electroscope" will be used to demonstrate the existence of the two types of charge and a few of their basic properties. In the second part, the attractive and repulsive forces that charges can exert on each other will be investigated. In the third part, a "Faraday pail" and charge sensor will be used to determine the sign of the charge resulting from rubbing objects together. OBJECTIVES

Demonstrate that a material can acquire a net charge by rubbing it with a dissimilar material.

Demonstrate that either of the two types of charge may be acquired, depending on the material, and demonstrate the forces that charges exert on each other.

Demonstrate that charge can be either transferred to an object or "induced" on an object.

Determine the signs of the charges acquired by rubbing two dissimilar materials together.

MATERIALS

various rods and rubbing cloths Faraday pail and charge sensor electroscope charge separators swivel Labquest Mini

connecting wires computer

PRELIMINARY QUESTIONS

1. If something is "charged," what does that mean?

2. If something is "neutral," what does that mean"

3. What happens if you have two positively charged objects near each other?

4. What happens if you have a positively charged object near a negatively charged one?

PROCEDURE

Part I Demonstrations with the electroscope

The electroscope, shown in Fig. 1, consists of a metal conducting rod with a

metal ball at the upper end and a pair of light, hinged, conducting leaves at

the lower end. The rod is insulated from the electroscope’s metal case by

an insulating stopper. If both leaves acquire either a net positive charge or

a net negative charge, they will separate due to the repulsive forces that the

leaves exert on each other. Fig. 1 shows the situation when the ball, rod,

and leaves have acquired positive charge. Figure 1

Insulator

Metal rod

Conducting leaves

+ + +

+

+

+

+

+

+

+

+

+

11

Before attempting each demonstration, touch the knob of the electroscope with your finger to

remove any excess charge it may posses. (Your body acts like a large reservoir for charge to go

to or to come from.) For each demonstration, draw sketches indicating the location of charges on

the different parts of the electroscope and explain your observations.

What to do if you get weak responses. Handling rods can result in contamination that allows

charge to leak away by conduction. Take the rods to a restroom and wash the unpainted length

with soap and water. Dry them thoroughly with paper towel. Back in the lab, dry them further

using a heat gun. Afterwards, do not touch the cleaned part except with the rubbing material.

1. For the following steps, wear a disposable latex glove when holding the painted end of any of the rods. Charge the plastic rod by rubbing it with a piece of cloth, and then touch the rubbed part to the electroscope’s metal ball. The plastic will have acquired a negative charge by the rubbing process.

2. Charge the plastic rod again by rubbing it with a cloth, and then bring it close to the electroscope’s metal ball without touching it.

3. Repeat steps 1 and 2 with the glass rod rubbed with tissue paper ("Kimwipes"). In this case, the glass acquires a positive charge.

4. Bring both the charged plastic rod and glass rod near the metal ball without touching, and see if you can adjust their relative distances from the ball to produce no divergence of the leaves.

5. To charge the electroscope by “induction”, bring the charged plastic rod near the metal ball, but not touching it, and then touch the ball with your finger. Remove your finger and afterwards withdraw the rod. To test the sign of the induced charge on the leaves, once again bring the charged plastic rod near the ball and see if the leaves collapse or diverge further.

Part II Forces that charged objects exert on each other

6. Rub one end of a plastic rod with a cloth and rest it on the swivel. Rub one end of another plastic rod and bring that end close to the rubbed end of the first rod. Observe whether there is attraction or repulsion.

7. Repeat step 6 with two glass rods rubbed with Kimwipes tissue paper.

8. Repeat step 6 with a plastic rod rubbed with cloth on the swivel and a glass rod rubbed with Kimwipes tissue paper brought close to it.

9. Place an uncharged metal rod on the swivel and bring a charged plastic rod close to one end. Observe whether there is attraction or repulsion.

10. Repeat step 9 with an uncharged plastic rod on the swivel. Compare the strength of the force on the plastic rod with that on the metal rod.

Part III Determining the sign of a charge with a Faraday pail

A Faraday pail set-up is shown in Fig. 2. The Faraday pail is the inner cylinder. The outer

cylinder shields the pail from the effects of stray charges in the environment. When, for example,

a positively charged object is placed inside the pail, it attracts electrons through the wire that

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connects the pail to the charge sensor. A

negatively charged object repels electrons

through the wire. In this way, the sensor can

tell the sign of the charged object in the pail.

11. Set up the apparatus as in Fig. 2. Connect

the Labquest unit to the computer. Press and hold the reset button on the charge sensor. This will remove any unwanted charge in the pail or sensor. Repeat this step every time before placing a charged object in the pail

12. Open the Logger Pro file "Electrostatics" in the folder Lab 01. Set the data collection duration to 60 s, and data collection rate to 10 Hz.

13. Press the button on the charge sensor in order to zero it.

14. Discharge the two charge separators by dabbing them on a damp cotton cloth. Start data collection and verify that the charge separators carry no charge by inserting them one at a time into the pail. DO NOT LET THE SEPARATORS TOUCH THE PAIL. Repeat the dabbing process if necessary.

15. Rub the charge separators together, restart data collection, then insert the gray one for about 5 s and then the white one for about 5 s, and finally both together (not touching) for about 5 s.

16. Sketch or print the graph.

ANALYSIS

Part I Demonstrations with the electroscope

1. For each step 1 through 4, sketch the conducting parts of the electroscope and the nearby rod, and show the distribution of charges on each.

2. Explain your observations for steps 1 through 5.

Part II Forces that charged objects exert on each other

3. What force, attraction or repulsion, do charges having the same sign exert on each other?

4. What force, attraction or repulsion, do charges having opposite signs exert on each other?

5. How do you explain your observations in steps 9 and 10?

Part III Determining the sign of a charge with a Faraday pail

6. What were the signs of the charge for the gray and white charge separators?

7. What was the net charge on the pair of separators?

Figure 2

To Lab Quest

13

14

Lab 2. Coulomb's Law

The electrostatic forces which you observed in Lab 1 were studied in detail by Coulomb in 1784. His experiments resulted in the empirical law named after him. It describes the forces that two small, particle-like, charged objects exert on each other, forces that depend on the magnitudes of the charges, q1 and q2, as well as the distance r between the charged particles. See Fig. 1. To attempt to explore Coulomb's Law using physical apparatus is fraught with difficulty, especially in south Florida. For this reason, you will be using a computer simulation instead.

Figure 1 OBJECTIVES

• Determine how the forces on the particles depend on their charges.

• Determine how the forces on the particles depend on the distance between them.

• Determine whether Newton's 3rd law is applicable to these forces.

• Obtain a value for the Coulomb law constant. MATERIALS

computer PRELIMINARY QUESTIONS

1. Why do you think that exploring Coulomb's law with physical apparatus is "fraught with difficulty, especially in south Florida?"

2. How would you expect the forces to depend on the magnitude of either charge?

3. How would you expect the forces to depend on the distance between the particles? Would it increase or decrease as the distance increases?

4. Do the signs of the charges play a role? Explain.

5. Do you think that the magnitude of the force on the larger charge is bigger than that on the smaller charge?

PROCEDURE

1. Open simulation “Electrostatic” in folder Lab02.

2. Learn how to move the charges, change their magnitude and sign, and change the distance between them. Note qualitatively how the forces are affected by these changes. You can also move the ruler. It's 10 m long, so the main divisions are spaced at 1 m, the same as the spacing of the grid lines.

q1 q2

r

15

3. Keeping the distance between the charges fixed, conduct an experiment to determine how the forces vary with the magnitudes of the charges. Try keeping one charge fixed and record the force as the other charge is varied. Then try several different combinations so that the product of the two charges, q1q2, covers a large range. You should obtain enough data to fill Table 1. Also record the distance between the charges in the table.

4. Open Logger Pro file "Coulomb's Law" in folder Lab 02. Enter your data, create a new column containing the product of the two charges, q1q2, then plot a graph of force versus q1q2.

5. Keeping the magnitudes of the charges fixed, perform an experiment to determine how the forces vary with the distance between the charges. Obtain a set of measurements for distances ranging from 2 m to 12 m in 1 m increments. Record your data in Table 2, along with the values of the two charges.

6. Enter your data in Logger Pro and plot a graph of force versus the distance, r, between the charges.

7. For each value of r, enter the values of a suitable function of r in the last column in data set 2 which you think will result in a linear plot of force versus this new function of r. Check that the new plot is indeed linear.

ANALYSIS

1. What did you observe about the magnitudes of the forces on the two charges. Were they the same or different? Does your answer depend on whether the charges were of the same magnitude or different? How does this relate to Newton's 3rd law?

2. What did you observe about the directions of the two forces? How did the directions depend

on the signs of the charges?

3. Print your three graphs.

4. The graph of force vs. q1q2 should be linear. To fit a line to this data, click and drag the mouse across the linear region, then click Linear Fit, .

4. Combine the slope of the line with the value of r in order to obtain the value (plus units) of the Coulomb law constant.

5. What was the function of r that resulted in your third graph being linear?

6. Combine the slope of this graph with the values of q1 and q2 to again obtain the value (plus units) of the Coulomb law constant.

16

DATA TABLES

Table 1 Distance between charges, r = m

q1 (C) q2 (C) Force (N)

Table 2 q1 = C q2 = C

Distance, r (m) m

Force (N)

17

Lab 3. Electric Field and Potential

Coulomb's Law describes the force that one charged particle exerts on a second charged particle. A more useful description includes the role of the electric field. It is preferable to say that the first particle produces an electric field in the space around it, and if a second particle is placed in this space, the field exerts a force on it. The strength of the field, E , at the location where the second particle was placed is defined as the force on that particle divided by its charge. A second related field that characterizes the space is electric potential, V. The relation between the two is that E is the "gradient" of V (the rate of change of V with position).

In this experiment, you will be mapping the potential in the space around a pair of charged objects and determining what information can be extracted regarding the associated electric field.

OBJECTIVES

Measure the potential at different points in the space surrounding different pairs of charged objects.

Generate, and familiarize yourself with the concept of, "equipotential lines."

Learn how to deduce E from the equipotential lines and the spacing between them. MATERIALS

glass try battery different shaped conductors connecting wires multimeter grid paper

PRELIMINARY QUESTIONS

1. What is meant by "voltage?"

2. If E is the gradient of potential, then 1 N/C should be the same as 1 V/m. Show that this is true. You may need to look up the definition of the volt.

3. What is the value of E inside a conductor, charged or uncharged?

4. What can you say about the potential inside a conductor, charged or uncharged?

INITIAL SET UP

1. Place the two pieces of L-shaped aluminum at opposite ends of the tray as shown in Fig. 1 to simulate two parallel plates. Three sheets of tear-out grid paper are provided in this manual following page 17. Place the tray on the grid paper and adjust the positions of the plates so that the vertical surfaces facing each other line up with the markings on the grid.

Figure 1

18

2. Add water to the tray leaving about a quarter inch of the plates above the surface.

3. Connect the negative terminal of the 9 V battery to the right plate. The connecting clip must not touch the water. For added stability, thread the connecting wire upwards through the slot in the tray handle.

4. You will be measuring potential with the multimeter which you should set to DC voltage (V) and the smallest range which exceeds 9 V. This will give you maximum sensitivity. The probes should be connected to voltage and ground terminals of the meter. Connect the ground probe to the negative plate and place the other probe in the water. The meter will record the potential difference between the probes. However, if we arbitrarily assign a potential of zero for the negative plate, then the reading on the meter will be the potential at the location where the other probe is placed.

5. CHECK WITH YOUR TA before making the final connection of the positive terminal of the battery to the left plate. Remember you are dealing with electricity and water which is a conductor, albeit a weak one. You have now established a potential of 9 V for the left plate relative to 0 V for the right plate. Check that this is so by touching the probe to each plate.

PROCEDURE

1. Place the probe vertically in the water and note on the meter how the potential changes as you move the probe from point to point.

2. Map the 2 V equipotential line by locating as many points as possible where the meter reads 2 V. Make a note of the coordinates on the grid paper where this occurs. Repeat for the 3, 4, 5, 6, and 7 V equipotential lines.

3. Disconnect the battery, then remove the grid paper and draw and label the equipotential lines.

4. Remove the parallel plates and repeat the above procedures with the two metal cylinders. This will be an approximate simulation of two oppositely charged particles. Center the cylinders over the circular markings on the grid paper so that you can map the equipotential lines around the cylinders as well as between them.

5. Remove the left cylinder and replace it with one of the plates. This will be an approximate

simulation of a charged particle in front of a flat plate. Map the equipotential lines as before.

ANALYSIS

1. On each of your equipotential maps, draw some electric field lines with arrow heads indicating the direction of the field. (Hint: At what angle do field lines intersect equipotential lines?) Draw sufficient field lines that you can "see" the electric field.

2. Describe the electric field between the parallel plates. Are there regions where it appears uniform? non-uniform? What is the value of E midway between the centers of the plates?

3. From the "density" of the electric field lines seen in the second two maps, how can you tell where E is large and where it is small?

4. From the spacing between the equipotential lines seen in the second two maps, how can you tell where E is large and where it is small?

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Lab 4. Capacitors

A capacitor is any two conductors separated by an insulator. If a potential difference, V, is

established between the conductors, charges +q and –q appear on the conductors. The

relationship between q and V is q = VC, where the constant C is the capacitance of the capacitor

measured farads, F, (1 F = 1 C/V). The capacitance depends on size, shape, and location of the

conductors as well as the insulating material. In this lab, we first build a parallel plate capacitor

and then investigate combinations of capacitors as well as the charging/discharging

characteristics of capacitors. A parallel plate capacitor consists of two flat conducting plates

placed on top of each other, but separated by an insulating layer. The capacitance of a parallel

plate capacitor is given by

d

A C 0

 =

where  is the dielectric constant of the insulator, 0 is the permittivity of free space, A is the

area of either plate, and d is the separation distance between the plates.

To study the charging/discharging properties of a capacitor, we’ll build an RC circuit with a

capacitor, resistor, and battery. We’ll connect a charged capacitor to the resistor and monitor the

charge flowing off one of the plates, through the resistor, and onto the other plate. OBJECTIVES

• Build and investigate the capacitance of a parallel plate capacitor.

• Investigate the capacitance of capacitors connected in series and in parallel

• Measure an experimental time constant of a resistor-capacitor circuit.

• Compare the time constant to the value predicted from the component values of the resistance and capacitance.

MATERIALS

aluminum foil resistor meter stick power supply multimeter current probe capacitors Labquest Mini

Vernier caliper computer

PRELIMINARY QUESTIONS

1. A good analogy to charging a capacitor would be filling a scuba tank with compressed air. What would be the quantities equivalent to q, V, and C in the relation q = VC?

2. In simple terms, why would you expect the capacitance of a capacitor to be proportional to the plate area?

3. Why would you expect the capacitance of a capacitor to be inversely proportional to the distance between the plates?

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PART 1: BUILD A CAPACITOR You can build a parallel plate capacitor out of two sheets of aluminum foil separated by a piece of paper. We’ll use textbook pages as the separator since it is easy to slip the aluminum foil between any number of pages, thus varying the separation distance. To ensure the aluminum foil sheets have uniform separation, place a weight on top of the book. Be careful not to “short out” the sheets of aluminum foil when you connect the meter leads to the sheets. That is, don’t let them touch each other.

PROCEDURE

1. Take two pieces of aluminum foil approximately the size of your textbook and measure their area. You may want to add small “tabs” for connecting to the multimeter leads. Place them in your textbook separated by 10 pages. They should be carefully aligned with each other. Note that if the areas are slightly different, the area that should be recorded in the data table is the area of overlap. You may want to add small “tabs” for connecting to the multimeter leads. Place a weight on the textbook

2. Attach two leads with alligator clips to the tabs. At your station is a meter that can measure capacitance. Select the capacitance measurement function ( symbol) on the meter. Attach the other ends of the leads to the meter and take a measurement of the capacitance.

3. Fill in the data table with your values.

4. To explore the relationship of capacitance to the separation distance, change the number of pages between the foils. You want to make an additional four (or more) measurements and record them in the table. Make sure to place the weight on the book for each measurement. Decide how to vary the numbers of pages, considering how the capacitance depends on separation distance.

5. To explore the relationship of capacitance to area, reduce the area of both pieces of foil equally, insert them into the book, and record your measurements in the table. You should carry out at least two additional measurements to study the trend. Decide how to vary the size of the foil. Again, consider how to optimize the measurements.

6. Estimate the thickness of the pages by using a Vernier caliper to measure a large number of pages and then determine the average values for the thickness. You may want to make several measurements and average the results.

ANALYSIS

1. Open the Logger Pro file "DIY-capacitor" in folder Lab 04, enter your data and plot a graph of the measured capacitance vs. the distance between the plates for the same plate area.

2. How does the capacitance depend on separation? Does it follow a straight line? Does it follow the trend you expect? Why or why not?

3. What should be plotted on the x and y axes to produce a straight line graph? Plot another graph to check your prediction. (The last column in the data table can be used to enter the appropriate values.)

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4. Plot a graph of the measured capacitance vs. the area of the plates for the same plate separation.

5. How does the capacitance depend on area? Does it follow a straight line? Does it follow the trend you expect? Why or why not?

6. Using the slope of this graph, together with the distance between the plates, determine the dielectric constant of paper. Find a value for the dielectric constant of paper on the Web or elsewhere and compare to your measured value. (Note that different types of paper could have different dielectric constants.)

PART 2: CAPACITORS IN SERIES AND IN PARALLEL

1. Use the multimeter to measure the capacitances of three capacitors

2. Connect the capacitors in series and measure the capacitance of the combination.

3. Connect the capacitors in parallel and measure the capacitance of the combination.

ANALYSIS

1. Calculate the capacitance of the series combination of capacitors and compare it with what you measured.

2. Calculate the capacitance of the parallel combination of capacitors and compare it with what you measured.

PART 3: INVESTIGATE DISCHARGING OF A CAPACITOR

A capacitor that has been previously charged by connecting it to a battery, can be discharged by connecting it to a resistor (a conductor that impedes the flow of electrons to a greater or lesser extent), a so-called RC circuit. As the charge on the plates decreases, so too does the voltage between the plates (because q = VC). Since it this voltage that drives the discharge, the rate of flow of electrons decreases exponentially with time. If we plot a graph of the rate of flow of charge (current) vs. time, the area under the curve is equal to the total amount of charge that has flowed which, if we wait until the flow has stopped, must be the same as the charge that was initially on the plates.

Fig. 1a Rate of flow of charge as function of time Fig. 1b Bar chart approximation of Fig. 1a

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Why is the area under the curve equal to the total amount of charge that has flowed? Hint: To answer this question, consider the bar chart in Fig. 1b which approximates the actual curve in Fig 1a. During each interval, t, the amount of charge that has flowed is equal to the rate of flow (height of column) multiplied by t (width of column), i.e. the area of the column.

PROCEDURE

Fig. 2 RC circuit.

1. Connect a series circuit of the resistor, capacitor, current probe and battery as shown in Fig. 2. Make sure the capacitor and current probe terminals labeled + and – are as shown in Fig. 2, and that the battery pack's red and black terminals are as shown. One end of the connecting wire, labeled A, from the resistor is shown disconnected. If the end A is connected to the battery's positive terminal, B, the battery will charge the capacitor through the resistor. If, subsequently, the end A is connected to the terminal C, the battery pack is eliminated from the circuit, and the capacitor will discharge through the resistor.

2. We now want to obtain a graph of the rate of flow of charge (current) as the capacitor discharges. Plug the third current probe lead into the Labquest unit, and plug the Labquest into a USB port on the computer.

3. Open the Logger Pro file "Capacitor" in folder Lab 04. A graph will be displayed. The vertical current axis of the graph should be rescaled, if necessary, from 0 to 0.1 amps. The horizontal axis has time scaled from 0 to 10 s. With end A still disconnected, zero the current probe by clicking the "Set zero point" button  on the toolbar.

4. Connect the end A of the connecting wire to the battery's positive terminal, B. The capacitor will become fully charged after about 10 seconds.

5. With A still connected to B, use the multimeter to measure the voltage between the plates. To do so, set the multimeter to DC volts, and then touch the multimeter probes to the terminals of the capacitor. Calculate the charge on the capacitor from the relation q = VC.

6. Disconnect the end A of the connecting wire from B (the capacitor will retain its charge), click to begin data collection, and immediately connect the end A to terminal C.

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7. You should obtain a curve similar to Fig. 1a, but with a zero current portion for the period before A was connected to C. Repeat steps 4 to 6 if necessary to obtain a good graph. The curve should have reached baseline. If necessary, rescale the horizontal time axis.

ANALYSIS

1. Using only the portion of the graph from the peak out to baseline (~ 10 seconds), determine the area under the curve using the integration button. Record it as the total charge that has flowed.

2. Print a copy of the graph of current flowing as a function of time.

3. How did the initial charge on the capacitor compare with the total charge that flowed?

4. How quickly the capacitor discharges depends, as you will learn later, on the "time constant" of the RC circuit. It is defined as the time taken for the current to decrease to 1/e of the initial value. (e = 2.718 is the base of natural logarithms.) From your graph, determine the time constant and enter the value in the table.

5. Theoretically, the time constant, t, can be shown to be equal to R times C (t = RC). If R is in ohms and C is in farads, t will be in seconds. Calculate the time constant, enter the value in the table, and compare it with the value from your graph.

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DATA TABLES

PART 1

Separation (m) Length (m) Width (m) Area (m2) Capacitance

PART 2

Capacitance (F)

(measured)

Capacitance (F)

(theoretical)

C1

C2

C3

Series combination

Parallel combination

PART 3

Initial charge on capacitor (C)

Total charge that flowed (C)

Time constant, measured (s)

Time constant, theoretical (s)

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Lab. 5 Ohm’s Law & Resistance

The fundamental relationship among the three important electrical quantities current, voltage, and resistance was discovered by Georg Simon Ohm. The relationship and the unit of electrical resistance were both named for him to commemorate this contribution to physics. One statement of Ohm’s law is that the current through a resistor is proportional to the voltage across the resistor. In this experiment you will test the correctness of this law in several different circuits using a Current & Voltage Probe System and a computer.

These electrical quantities can be difficult to understand because they cannot be observed directly. To clarify these terms, we can make the comparison between electrical circuits and water flowing in pipes. Here is a chart of the three electrical units we will study in this experiment.

Electrical Quantity Description Unit

Water Analogy

Potential Difference or

Voltage

Potential energy

difference/unit charge of a

charge at two points in a

circuit.

Volt (V)

1 V = 1 J/C

Water pressure difference

between two points in a pipe

Current Rate of flow of charge through

a conductor.

Ampere (A)

1 A = 1 C/s

Rate of flow of water

through a pipe

Resistance A measure of how difficult it is

for charged particles to flow

through a conductor.

Ohm () A measure of how difficult it is for water to flow

through a pipe.

OBJECTIVES

• Determine the mathematical relationship between current, potential difference, and resistance in a simple circuit.

• Compare the potential difference vs. current behavior of a resistor to that of a light bulb and light emitting diode (LED).

MATERIALS

computer two resistors (about 56 and 82 ) Labquest Mini connecting wires adjustable 6-volt DC power supply light bulb (6.3 V) current probe & voltage probe LED

PRELIMINARY QUESTIONS

1. A TV news reporter once stated that a person was electrocuted "when 20,000 volts of electricity surged through his body." What is wrong with this description? What was it that "surged" through his body?

2. Do you expect the resistance of a light bulb to remain constant as the current through it is increased and the filament goes from red-hot to white-hot? Explain why or why not.

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3. The definition of the resistance of a conductor is R = V/I, where V is the potential difference between its ends and I is the resulting current through it. Ohm's Law, as an equation, states that V = IR. The two equations look the same. What is the difference?

PRELIMINARY SETUP

The resistance of a resistor is often indicated by a series of colored bands painted on the body of the resistor. The colors of the bands indicate numbers: black = 0, brown = 1, red = 2, orange = 3, yellow = 4, green = 5, blue = 6, violet = 7, gray = 8, white = 9. A "tolerance" band is indicated by silver (±10%) or gold (±5%). If you orient the resistor with the tolerance band on the right, the two leftmost bands give the first and second digits, and the third band gives the number of following zeros. So if the band colors are red, green, black, and silver, the resistance is 25  and the tolerance is ± 10%.

1. WITH THE POWER SUPPLY SWITCHED OFF, connect the power supply, 56  resistor, wires, and clips as shown in Figure 1. Take care that the positive lead from the power supply's DC output and the red terminal from the Current and Voltage Probe are connected as shown in Figure 1. Note: Attach the red connectors electrically closer to the positive side of the power supply.

2. Connect the outputs from the current probe and voltage probe to the Labquest unit and connect the Labquest unit to the computer.

3. Open the Logger Pro file "Ohm's Law" in the folder Lab 05. A graph of potential difference vs. current will be displayed. The horizontal axis is scaled from 0 to 0.6 A. The Meter window displays potential and current readings.

4. Click the "Set zero point" button  on the toolbar. A dialog box will appear. Select the two sensors and click "OK." This sets the zero for both probes with no current flowing and with no voltage applied.

5. HAVE YOUR INSTRUCTOR CHECK YOUR SET-UP BEFORE PROCEEDING.

6. Turn the control on the DC power supply to 0 V and then turn on the power supply. Slowly increase the voltage to 6 V. Monitor the Meter window in Logger Pro and describe what happens to the current through the resistor as the potential difference across the resistor changes. If the voltage doubles, what happens to the current? What type of relationship do you believe exists between voltage and current?

Power supply+ -

I Resistor

BlackRed

Current probe

Voltage probe

Red Black

To LabquestVoltage probe

Figure 1

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PROCEDURE

1. Record the value of the resistor in the data table.

2. Make sure the power supply is set to 0 V. Monitor the voltage and current. When the readings are stable, record the voltage and current in the data table.

3. Increase the voltage on the power supply by approximately 0.5 V. Again when the readings are stable, record the voltage and current in the data table.

4. Repeat step 3 until you reach a voltage of 6.0 V.

5. In LogPro, enter current and voltage from the data table in the columns 'Current (graph)' and 'Potential (graph),' respectively. Print a copy of the graph.

6. Are the voltage and current proportional? Click the Linear Regression button, . Record the slope and intercept in the data table. Click the Curve Fit button, . Choose 'Proportional Fit.' Record the slope and error in the data table.

7. Repeat Steps 1 – 6 using an 82  resistor.

8. Replace the resistor in the circuit with a 6.3-V light bulb and repeat Steps 2 – 5, but this time plot current on the y axis and voltage on the x axis. (Double left click on the graph and make changes under "Axes Options'.) Print a copy of the graph. Calculate the effective resistance for each pair of measurements.

9. You are provided with a transparent box containing a light emitting diode ( LED) in series with a protective resistor. Turn off the power supply and set up the circuit shown in Figure 2. Make sure you connect the power supply's positive terminal to the red socket on the box. Connect the red lead from the voltage probe to the red socket on the box and the black lead to the central tab on the box. You will then be measuring the voltage across the LED only.

10. Turn on the power supply and make a series of voltage and current measurements as before, but at 0.2 V intervals once the current begins to increase. Plot and print a graph as you did for the light bulb (current on the y axis, voltage on the x axis).

Figure 2

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ANALYSIS

1. As the voltage between the ends of the resistor increased, the current through the resistor increased. If the current is proportional to the voltage, the data should lie on a straight line passing through the origin. For the two resistors, how close is the y-intercept to zero? Is there a proportional relationship between voltage and current? If so, write the equation for each resistor in the form potential difference = constant  current. (Use a numerical value for the constant.)

2. Compare the constant in each of the above equations to the resistance of each resistor.

3. Resistance, R, is defined using R = V/I where V is the voltage across a resistor, and I is the current. R is measured in ohms (), where 1  = 1 V/A. The constant you determined in each equation should be similar to the resistance of each resistor. However, resistors are manufactured such that their actual value is within a tolerance. Examine your resistors' color codes to determine the tolerance of the resistors you are using. Calculate the range of values for each resistor. Does the constant in each equation fit within the appropriate range of values for each resistor?

4. Do your resistors follow Ohm’s law? Base your answer on your experimental data.

5. Describe what happened to the current through the light bulb as the voltage increased. Was the relationship linear? Determine the resistance at each voltage and enter the results in the data table. Describe what happened to the resistance as the voltage increased. Since the bulb gets brighter as it gets hotter, how does the resistance vary with temperature?

6. Does your light bulb obey Ohm’s law? Base your answer on your experimental data.

7. Describe what happened to the current through the LED as the potential difference increased. Was the relationship linear? Determine the resistance for each voltage and enter the results in the data table. Describe what happened to the resistance as the voltage increased.

8. For the maximum voltage settings in each case, calculate the corresponding electrical power, P, being consumed by the light bulb and LED. (Recall that P IV= .) P represents the rate at which electrical energy is being converted into other forms, such as light and thermal energy. Which device appears to be more efficient at producing light?

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