PHYS 1420: College Physics II
Fall 2009
Lab 07: Faraday’s Law of Magnetic Induction
Introduction
Faraday’s Law is the key to the castle. If the castle you are trying to unlock happens to be Maxwell’s equations. Ok, so we
are not going to immerse ourselves in Maxwell’s vector calculus, but Faraday’s Law is perfect for proving to ourselves that
you cannot separate the electro– from the –magnetic. According to Faraday’s Law, a changing magnetic flux will create a
voltage across a loop of wire. Or, changing the voltage across
(alternately, the current through) one loop of wire will induce a
voltage across (alternately, a current through) another loop.
Which draws us inexorably toward alternating current, motors,
generators, and the twentieth century in general.
Objectives
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Demonstrate the connection between electricity and magnetism
Define magnetic flux
Use a solenoid to generate a magnetic field
Prove Faraday’s Law
Equipment
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The solenoid will create a uniform magnetic field when a
current passes through the wire:
B=
Oscilloscope
Electronic function generator
Solenoid coil
Pickup Coil
Assorted wires
Experimental Procedure
1)
2)
µ o NI
L
The solenoid has a length L (you measure this) and N=60
turns.
Wire the function generator to the solenoid. Notice that
€ hardwired to one end of the solenoid.
there is a resistor
The resistor puts a constant load across the circuit. The
known resistance permits us to use Ohm’s Law to find the
current
I=
V
R
3)
make the loop larger or smaller;
change the orientation of the loop: rotate it to trap
more or fewer lines;
change the magnetic field: increase or decrease B
to change the number of lines.
We will use a fixed loop as a pickup coil, so the geometry
of the loop is designed to maximize the flux. The maximum number of lines will be trapped if the plane of the
loop is perpendicular to the field lines. Our pickup coil is
concentric with the solenoid, which makes it perpendicular
to all of the field lines. The diameter of the pickup coil is
only slightly smaller than the solenoid diameter.
Neither of these parameters will change, so we will vary
the magnetic field created by the solenoid:
 AΔB 
emf = n

 Δt 
The magnetic field of the solenoid is then:
€
B=
µ o NV
RL
According to Faraday’s Law, changing a magnetic field can
induce an emf (voltage) in a loop of wire. The more coils
in the loop of wire (pickup coil n = 55), the greater the
induced emf.
€ The greater the rate of change of the magnetic flux, the greater the emf:
 ΔΦ 
emf = n

 Δt 
What is magnetic flux? Think about using the loop of wire
to “trap” the magnetic field lines generated by the solenoid. The greater the area of the loop, the more field
lines you €
will “lasso.” The stronger the magnetic field, the
more field lines--the more lines can be trapped. The rate €
of change means that, over time, the amount of trapped
lines changes. You can change the number of trapped lines
several ways:
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The magnetic field is easy to change; simply change the
current through the solenoid.
This is where the function generator comes in. The func€ can be set to provide a signal that varies in
tion generator
a known way. We will use the triangular or sawtooth function: this gives you a linear increase in voltage, followed
by a linear decrease. The generator allows you to adjust
the frequency and amplitude of the signal:
ΔB =
µ o NΔI
L
OR
ΔB =
µ o NΔV
RL
By measuring the changing voltage, we measure the changing field.
This is where the oscilloscope comes in. The oscilloscope
€ the signal through the solewill show us graphically both
noid and the emf in the pickup coil.
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PHYS 1420: College Physics II
‣
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Fall 2009
Attach the oscilloscope (channel 1) to
the solenoid (like the voltmeter, this
goes in parallel). Set the function generator frequency range to 2k Hz. You
should see the sawtooth wave form on
the screen.
Adjust the volts/div scale on the scope
to 5 volts/div. Use the output level
knob on the function generator to adjust the amplitude of the wave. Make
the wave 10 volts peak-to-peak, or two
divisions tall.
The frequency of the wave is adjusted
using the large dial. Adjust the frequency and note what happens to the
wave on the scope screen. You may
need to adjust the time/div scale as
well; you should see several cycles of
the wave with no flicker (you may also
need to adjust the trigger level very
slightly to eliminate flicker).
Attach the pickup coil to scope channel 2. The induced emf is very small, so you will need to adjust the volts/div
scale to 10mV/div or 20 mV/div. You should see a pattern of flat (constant emf) signal plus or minus that corresponds to the sawtooth wave. The peak-to-peak voltage is twice the induced emf.
Data
Make a table of induced emf as a function of time. Measure the peak-to-peak induced emf, then remember to divide it
half. The time is measure for one half of a complete cycle: the time as V increases. You may adjust the position of each
beam to make recording the measurements as easy as possible.
Change the frequency of the sawtooth wave, then record the time and emf. Continue to increase the frequency gradually
and record emf. You may need to slightly adjust the output level to keep the sawtooth at 10V peak-to-peak, and you may
need to adjust the volts/div to measure the emf or the time/div scales. You should get between 8 and 10 data pairs.
Reduction and Analysis
If the mathematical development above is valid, then the data should be linear:
  µ o NΔV  

 A
 RL  

emf = n
Δt






OR
 µ nNAΔV  1
emf =  o


 Δt
RL
Remember that frequency is the inverse of period, so emf is directly proportional to frequency, or the inverse of the measured time. Graph your data with emf on the y axis, and the inverse of time on the x-axis. Find the slope and intercept of
the graph. This can be done using whatever appropriate graphing tool you have.
€ of the experiment:
We can predict the€
slope based on the constant parameters
 µ nNAΔV 
slope =  o



RL
Where A is the area of the pickup coil, which is:
€
Why not just
πr2?
A=
π 2
ro + ro ri + ri2 )
(
3
Because the wire coil has an inner and outer diameter!
This means you will need to measure the inner and outer diameters of the pickup coil, as well as the length of the solenoid.
Use the ruler for length, calipers for diameters. Record the uncertainties! Even though the solenoid voltage remains con€
stant, you should also include the uncertainty
based on the scale of the oscilloscope (± half the smallest division). The time
should also have an uncertainty associated with it. This means that both your experimental slope and predicted slope will
have uncertainties associated with them.
Report your data, graph, and error analysis.
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