Faraday`s Law - Penn State University

Faraday's Law

Objective:

In today's experiment you will investigate electromagnetic

induction and determine the factors that affect it.

Theory:

The phenomenon of electromagnetic induction was first studied

independently by Henry (American) and Faraday (English) in the 19 th

century. Generally Faraday is given credit for the discovery since he

published his discoveries sooner than Henry.

Electromagnetic induction is the phenomenon whereby a fluctuating

magnetic flux through a coil of wire generates an emf (electromotive

force) in the wire. In other words, if you push a bar magnet through a

coil of wire, you will generate electricity. This is the fundamental

principle behind the generation of electricity in today's commercial

power plants.

Both Faraday and Henry realized that the emf generated could

depend on 1) the number of loops in the coil of wire, 2) the strength of

the magnetic flux, and 3) the rate at which the flux fluctuates.

The experiment that follows will investigate each of these things.

Pay close attention, follow directions carefully, and accurately record

your data. See if you agree with Faraday's and Henry's conclusions:

ε = −

N

∆Φ

B

∆

t

Apparatus:

1) bar magnet;

2) coil of magnet wire (20 or 22 awg);

3) three rectangular ceramic magnets;

4) a spring system;

5) slot weight system;

6) two large binder clips;

7) Pasco Science Workshop software and interface

8) Voltage leads

9) Motion sensor

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2000 Kip Trout Project development was supported by an NSF-ILI Grant “Interactive, Microcomputer-Based Undergraduate Physics Laboratory”

Grant No. DUE-9851024 Any opinions, findings, conclusions or recommendations expressed in this document are those of the author, and do not necessarily reflect the views of the National Science Foundation.

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PROCEDURE:

Part I - Lenz's Law and the Induced Current

1. Boot up the computer (if necessary) and logon. Open Science Workshop .

2. Take a good look at your experimental setup. You will need to return it to this

arrangement later in the experiment (step 8). But for now, unhook your spring from

the lab stand and lay the entire assembly (spring, binder clips, magnets and slot weight

hanger) on your lab table out of the way.

3. Goto file/open and then choose to look on the t: drive. Open the setup file frdy1-1

which you will find in the 151 Lab folder on the t: drive.

4. Now grab the bar magnet so that the red end (north pole) points downward, as though

it were an arrow head on an arrow. Start the data collection by double clicking REC .

Now center the magnet above the loops and thrust the magnet downward toward the

loops from above. (The north end of the magnet should be approaching the plane of the

loops first.) Watch the computer monitor as you do this. You should see a voltage peak

displayed on your screen. Now pull the magnet upward and watch the display again.

Repeat this down and up motion of the magnet several times, being careful to note the

polarity of the voltage peak when you move the magnet down and up. Stop the data

collection by double clicking on STOP . Now record what you have observed in the

provided data chart at the end of this handout.

NOTE: The coil of wire is labeled with an arrow . This arrow represents the

direction current flows through the loops when you get a positive voltage

deflection showing on your display. Naturally the current flows in the

opposite direction when you get a negative voltage deflection on your display.

5. Repeat the process in step 4, except this time hold the magnet so that the silver end

(south pole) points downward. Carefully observe the polarity of the voltage that is

associated with up and down motion of the magnet and record your observations in the

data chart.

6. Study the chart you have just filled in. Write a rule in the box below the chart that

describes the direction the induced current will flow in the loops when compared to the

direction that the magnetic flux was changing.

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3

NOTE: If you get this rule right, it should agree with Lenz's Law as

described in your textbook.

7. Now start the data collection by double clicking REC and move the magnet up and down

like you did in steps 4 and 5. Now move the magnet up and down very quickly. Now do it

slowly. Now STOP the data collection. Scroll back through the data. What do you note

about the size of the induced voltage as compared to the speed with which the magnet

is moved? Record your observation in the appropriate box on your data page.

Part II - Harmonic Motion and EMF

8. Now reconnect your spring, magnet and slot weight combination onto your lab stand.

Adjust the position and height so that the slot weight hanger is centered on the loops,

but hangs below the plane of the loops, while the bottom magnet is about 2 inches

above the plane of the loops .

9. Place the motion sensor on the floor. Align it with the center of the loops. Make

sure the motion sensor's switch is set on NEAR , and swivel the motion sensor so it

points directly upward.

10. Open setup file frdy1-2 which is on the t: drive in the 151 Lab folder.

11. Make sure the spring/magnet arrangement is not moving and start REC data for a few

seconds. STOP and then use the statistics function (

∑

) in the software to find the

MEAN of the data. This will be your reference height . Record it in your data chart.

12. Now, with an empty slot weight hanger (M = 50 grams), pull down until the bottom

magnet is very near the plane of the loops, but not penetrating the plane of the loops.

13. Release the system so that it oscillates up and down, and almost instantaneously double

click REC to start collecting data. Record data for roughly 30 seconds and then STOP.

14. Determine the period and frequency of your motion. To get the period, rescale the

time axis as necessary and get a good reading of the time for 10 complete cycles on

the position graph and then divide by 10. You may find the "cross hairs" ( ) function in

the software helpful in picking the times off the graph in this lab. The frequency is of

course the inverse of the period. Record these values in your data chart.

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4

15. Now scroll back toward the middle of your data (t = 15 seconds?). Highlight several

peaks in the middle of your voltage graph by holding down the left button of the

mouse and drawing a rectangle around them. (They should all be highlighted at the

same time, inside the same rectangular region.) Then use the statistics function to

determine the maximum value. Record this voltage in your data chart. Then print out

your graph showing this data region.

16. For the same time interval highlighted in the previous step, determine the maximum

and minimum positions on the position graph . This range of the motion will be

important later, so record these values in the data chart.

17. Now add 100 grams to your slot weight hanger. This will stretch the spring and cause

the magnets to be in a lower position. Loosen the appropriate thumb screw on the

shaft of the lab stand and move the assembly upward until the lower magnet is once

again about 2 inches above the plane of the loops.

18. Make sure the spring-magnet assembly is at rest and double click REC and take several

seconds of data. Click STOP and then use the statistics function to look at the

average position. Compare this to your reference height. Readjust the height of the

assembly as necessary until the average position is within 0.002 meters of your reference height .

19. Now, trying to be as consistent as possible with the previous trial, pull the magnets

down until the lower magnet is close to, but not penetrating through, the plane of the

loops, as before. Release the apparatus setting it into harmonic motion and almost

simultaneously click REC to start taking data. Collect data for about 30 seconds and

then click STOP .

20. Determine the period and frequency of your motion. To get the period, rescale the

time axis as necessary and get a good reading of the time for 10 complete cycles on

the position graph and then divide by 10. You may find the "cross hairs" ( ) function in

the software helpful in picking the times off of the graph. The frequency is of course

the inverse of the period. Record these values in your data chart.

21. Looking at the position graph , scroll through the data and find a region in the data

where the range of the motion (min. and max. positions) nearly match that found in

step 16. Note the time interval where this match occurs. Then highlight the peaks on

the voltage graph during this time interval and use the statistic function to determine

the maximum voltage. Record this value on your data chart. Then PRINT out your

graph showing this data region.

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5

22. Repeat steps 17 - 21 adding 100 additional grams each time. Stop when you get to

450 grams total load, or when your apparatus can no longer be adjusted to the proper

reference height. Record all data in the appropriate data table.

23. Now, leaving everything else unchanged, move the spring-magnet assembly down until

the middle magnet is centered on the plane of the loops. Pull down slightly and start

REC data. STOP after about 15 seconds. Determine the period and frequency for

this set of data. Why has the frequency doubled from its previous value? Give your

best explanation for this in the appropriate box on your data page.

Part III - Magnetic Flux and EMF

24. Now unhook your spring-magnet assembly and lay it off to the side somewhere on your

lab table. Also, place the motion sensor up on your lab table out of the way.

25. Open setup file frdy1-3 which is on the t: drive in the 151 Lab folder.

26. Make sure your magnetic field sensor is set on RADIAL . Then double click on REC and

start taking some data. Make sure there are no magnets close to the magnetic field

sensor and then press the ZERO button on your magnetic field sensor. Verify that it

has zeroed by looking at the field strength data display. Then double click STOP .

27. Find the white dot near the tip on your magnetic field sensor. Hold the sensor shaft

so the white dot is upward and place it in the center of the loops just below the plane

of the loops, but as close to them as possible. Be sure the white dot is centered in

the loops and pointing upward.

28. Take a bar magnet in your other hand and orient it so that the north pole is pointing

downward toward the white dot from above the loops (similar to step 4). Center the

magnet over the white dot about 1 inch above it.

29. Double click REC and start taking data. Move the magnet up and down over a

distance of about one inch as quickly as you can. Come as close to the magnetic field

sensor's shaft as you can without actually running into it, while keeping the magnet

directly above the white dot at all times. STOP after you have collected several

seconds of decent data. PRINT out a section of your good data.

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6

Note: Only if you failed to pick up any fluctuation in the magnetic field strength and are

sure you have been following procedure, you may try turning the magnet over so

that the south pole (silver end) is closer to white dot on the magnetic field sensor

and repeat the process.

30. Now scroll back through the data until you get to a section of good data. Examine it

carefully and answer the following question: When the voltage graph shows a

maximum or minimum voltage peak, what does the graph for the field strength look

like at the same time? For example, Is it peaking also? Does it read zero? Or is it

changing such that there is an upward or downward slope to the graph? In other

words, what does it take to produce an emf: Just a magnetic field, or does it take a

changing magnetic field? Write a rule that relates the slope of the field strength

graph to the voltage induced in the loops. Write this rule in the appropriate box on

your data page.

Note: The last part of the lab requires you to team up with another lab group.

If there is not a group ready to team up with you, then move on to the

ANALYSIS section and then come back to the steps you missed in the

procedure.

Part IV - The Number of Loops, the Flux Strength and EMF

31. Team up with another lab group. Put the magnetic field sensor out of the way and then

pull a padded chair up beneath your loops so that a bar magnet dropped through the

loops will be caught by the padded chair. Try not to let the magnet fall all the way to

the floor in this last part of the experiment.

32. Open up frdy1-4 on the t: drive in the 151 Lab folder.

33. Dangle a bar magnet between your fingers so that the north pole (red end) is pointing

downward. Center the magnet on the loops and place the north pole (red end) of the

magnet just barely above the plane of the loops. Double click REC and drop the

magnet straight downward through the center of the loops. STOP the data collection.

34. Scroll back through the data to find the voltage pulse that you created. Measure the

peak voltage and record this value in your data chart.

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7

35. Now repeat steps 33 and 34 with the other group's bar magnet. Be sure the north

pole (red end) is pointing downward and be sure to release from the SAME HEIGHT.

36. Now stack both magnets together with their red ends (north ends) held together and

pointing downward (as you have previously been orienting them). Repeat steps 33

and 34 except drop both magnets together through the loops. Be sure to release

from the SAME HEIGHT AGAIN.

37. What did you observe? Was the peak voltage affected by the nearly doubled field

strength? How so? Write a rule that you think describes how nature is behaving in

this situation (i.e. write your best explanation for what you just saw). Put your

answer in the appropriate box on your data page.

38. Now repeat steps 33 and 34 with one magnet again. Record the voltage in the

appropriate part of your data chart (labeled steps 38 - 40). It should be similar to

the previous trial using this magnet if you drop it from the SAME HEIGHT.

39. Take the second group's coil and remove it from the ruler supports. Lay it directly on

top of the first group's coil so that the current directions agree. Using the jumper

cable at your station, clip the negative side of coil 1 with the positive side of coil 2.

Now move the voltage leads so the positive lead (red) is clipped to the positive side of

coil 1 and the negative lead (black) is clipped to the negative side of coil 2.

40. Now using the same bar magnet as in step 38, orienting it in the same way (north end

down), dropping it from the SAME HEIGHT, double click REC and take data as you

drop the magnet through the center of the two sets of loops. STOP . Record the peak

voltage in the appropriate place in your data chart.

41. The number of loops was just about doubled in the previous step. How was the induced

voltage affected? Write a rule that you think best describes how nature is behaving

in this situation. Write your answer in the appropriate box on your data page.

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Steps 4 - 5

Direction of

Magnet's

B-Field

Up Down

Step 6

Rule

:

Step 7

Observation:

Direction of

Magnet's

Motion

Up

B-Flux Change Magnet

Motion Causes

(e.g. increasing down)

Down Increasing Decreasing

Direction of

Induced Current

(Viewed From Above)

CW CCW

B-Flux Direction

Caused by

Induced Current

Up Down

8

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Steps 8 - 22

Reference Height:

Range of Motion: Lowest: Highest:

Mass (g) Period (s) Frequency (Hz)

50

150

250

350

450

Step 23

Mass (g) Period (s) Frequency (Hz)

Step 30

Rule:

Steps 33 - 36

Magnet Dropped

A

B

A and B

Peak Voltage (V)

Peak Voltage (V)

Peak Voltage (V)

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9

Step 37

Rule:

Steps 38 - 40

Loops

80 (1 Coil)

160 (2 Coils)

Peak Voltage (V)

Step 41

Rule:

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10

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ANALYSIS:

1. Close Science Workshop and open up Vernier's Graphical Analysis software. If you are

doing this somewhere other than Penn State's physics lab, you may use a spreadsheet

software or some other graphing software.

2. Enter your data from steps 8 - 22 into the graphing software. Put the frequency value

in the X data column and the peak voltage in the Y data column.

3. Do a linear curve fit and print out your graph.

4. Assuming the number of loops in your coil of wire was about 80, and using your graph

you just printed out as needed, calculate the magnetic flux change that was occurring

as you oscillated the magnets back and forth in steps eight through twenty two. Show

your calculation and explain your reasoning step by step.

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5. Below write a general conclusion (rule for how nature is behaving) for each section of

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the lab. For example, for Part II you may have found, "The faster the magnetic flux

fluctuates, the greater the…"

Rule Observed

Part I

Part II

Part III

Part IV





Faraday`s Law - Penn State University

Faraday's Law

Objective:

Theory:

ε = −

∆Φ

∆

Apparatus:

PROCEDURE:

∑

ANALYSIS:

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Faraday`s Law - Penn State University

Faraday's Law

Objective:

Theory:

ε = −

∆Φ

∆

Apparatus:

PROCEDURE:

∑

ANALYSIS:

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