Experiment 10: Electromagnetic Induction
(There is no printed answer sheet for this lab. Do the calculations and discussion on regular paper,
and attach data and graphs printed by Excel.)
As one coil induces a voltage in another, we will investigate whether Faraday's law correctly
predicts how the voltage varies with distance, and how it varies with frequency. We use a function
generator to put an alternating current through the primary, and measure the voltage induced in the
secondary with an oscilloscope.
THEORY: Start by finding an expression for the amplitude of the induced voltage. (This lab can
be kind of long. Doing this ahead of time would be a good idea.)
1. If Io is the amplitude of the current in the primary, and f is its frequency, then the current in
the primary is I = Io cos(2πft). Substitute this into the equation for B from a flat coil. (Don't fill
in numbers; just call the radius R, the number of turns N, and so forth.)
2. Use this and the formula for a circle’s area to obtain an expression for the approximate flux
through the secondary, Φ. (Approximate, because these are not exactly flat coils, and because
the formula only gives the field on the primary's axis, not all over the secondary.) θ will be
kept at 0 throughout the experiment.
3. Put Φ into Faraday's law to get an expression for ε, the voltage induced in the secondary.
Since you are differentiating with respect to time, treat only t as a variable. Treat quantities
such as x or f which are not functions of time as constants.
4. Compare your formula for ε as a function of time to the general form ε = εmax sin (2πft) and
write down the formula for εmax. This is the expression you will experimentally check. You
should probably have the instructor check it before going on.
EXPERIMENT: Set this circuit up. The
resistor must be connected to the ground
(black) side of the function generator. Turn
things on and adjust them until you can
observe the induced voltage on the scope.
(See lab 9 for how to use the oscilloscope.
If faced with a blank screen, check the
following:
Is intensity turned up far
enough? Is y position set so that the trace is
beyond the top or bottom of the screen?)
Part A. Check your prediction of how εmax changes with distance:
1. Adjust the function generator's frequency and amplitude so that the induced amplitude is at least
250 mV when the coils are right together. (Peak-to-valley voltage of at least 500 mV.)
2. Measure the induced voltage at different distances, x, between the coils, keeping all other
variables constant. Note that x is the center to center distance. Be careful your finger does not
touch the signal wire from the secondary; you can act like an antenna, affecting your readings.
Take data from as close as possible to as far as possible: Your last reading should be 5 mV or less.
Review: To read voltages
from the oscilloscope:
a. Be sure variable y
amplitude (red knob
with an arrow) is fully
counterclockwise.
b. Read the peak to valley distance from the screen: 4.4 cm in this example.
c. Multiply by the y-amplitude knob’s setting. (It’s black.) For example, (4.4 cm)(2 V/cm) = 8.8
V. This makes the amplitude 4.4 V
3. Have Excel plot your measurements for εmax as a function of x, and also have it plot your
equation on the same graph. (Or, graph them by hand, but a spreadsheet makes it easier.)
a. In Excel, use the first row for headings: x in column A, measured εmax in column B,
calculated εmax in column C. (Abbreviate so they fit.) Enter your data in the first two columns.
Have it in order from closest to farthest, or it will make a strange looking graph.
b. For column C: Your formula should look like this:
“Constant” means something that did not change in this part of the experiment. Rather than
finding all of the constants one at a time, use the data point at the start of the graph and R = 2.2
cm to find the whole bunch at once:
Example: If your closest data point was x = 4 cm, ε = 600 mV (your x would be smaller),
In column C, you would then type =57100/(4.84 + a2^2)^1.5 This forces the experimental and
theoretical curves to start at the same point. Your objective is to see if experimental follows
theoretical from there. After typing this formula in row 2, copy it to the cells below. Show
how you obtained this formula in your report.
c. To create a graph: Highlight the first two columns. Click on insert, then scatter, then the
choice at upper right: “Scatter with smooth lines and markers”. Right click on the graph. Click
select data, then click edit, then put “measured” for the series name, then click ok. Click add
then put “Theoretical” for the name of the other series. Click in the x values box then outline
the numbers in column 1. Click in the y values box, delete what’s already in it then outline the
numbers in column 3. Click ok twice. Drag the graph to below the data so it prints on the same
page. Click somewhere outside the box, or it will just print the graph without the data table.
d. Print a copy for each person in the group: Click file, then print. Check that the preview
shows both the data table and the graph, select the number of copies, then click the print button.
4. In your conclusion, comment on whether the experimental graph matches the theoretical one.
Part B. Check your prediction of how εmax changes with frequency:
You want f to be the only variable which changes between trials. If you aren't careful, the current,
I0, will also change because the "impedance" of the coil (section 12) changes with frequency. To
monitor I0, press Dual on the scope. It now shows both channel 1, where you will get your data, and
channel 2, the voltage across the resistor, which is proportional to I0.
Start with something high like 50 000 Hz, because I0 goes down as f goes up. Set the function
generator to produce the largest amplitude it can, and notice what that amplitude (on channel 2) is.
As you take readings at other frequencies, keep adjusting the function generator's attenuation so that
channel 2 always has this same amplitude. Then f will be the only variable.
So, 1. With the two coils right against each other, measure the induced voltage at a wide range of
different frequencies (make your highest f at least 100 times your lowest). Be sure to adjust I0 to the
same value for each trial.
2. If you’re done with part A, just type this new data over the old in the same spreadsheet. (Change
the column heading from x to f.)
3. For column C: Your formula should look like this: εmax = (a bunch of constants)f. x is now a
constant and f is not. Use the point with the highest frequency to find this “bunch.” Put the formula
in column C using the number you determined. Print.
4. In your conclusion, comment on whether the experimental graph matches the theoretical one.
Checklist. Include in your report:
1. Calculations: (a) Step by step derivation of your general formula for εmax, (b) How you got the
formula you put into the spreadsheet for part A, and (c) How you got the formula for part B.
2. Printouts from Excel showing your data tables and graphs for each part.
3. Your discussion of the experiment.