Lab 4: Magnetic Measurements and Faraday's
Law
NAME________________NAME__________________NAME________________
Introduction
Faraday's law states that a voltage e(t ) is induced at the terminals of a coil
that "sees" a time-varying magnetic flux Φ(t ) (Text p.255):
e(t ) = −
dΦ (t )
dt
(1)
For an N-turn coil, each turn having an area A, the magnetic flux is
Φ(t ) = B(t )NA , where B(t ) is the magnetic field. If the coil voltage e(t ) is
electronically integrated, then
t
1
Vout (t ) = −
e(t ')dt '
RC ∫0
(2)
where RC is the time constant of the integrator. Combining (1) and (2), we
obtain
Vout (t ) = −
1
NA[B (t ) − B (0 )]
RC
(3)
If B(0) = 0 , then
B(t ) = −
RCVout (t )
NA
(4)
In this lab you will insert a coil into the static magnetic field of a solenoid
(or turn on the magnetic field with the coil in place) and use (4) to determine
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the magnetic induction B(t) along the solenoid axis. You will compare to
measurements made using a Bell 615 Gaussmeter.
Qualitative Observations:
1. Connect the 10-turn, 3.5-cm diameter coil to the Tektronix 549
storage oscilloscope. The induced voltage waveform can be observed
on the scope when the coil is swung through an area with magnetic
field.
The scope settings and observing procedures are:
(a) Triggering Setting: A trigger mode = auto, Slope = +,
Coupling = AC, Source = int. normal.
(b) Horizontal Display: Time base A at 0.1 sec/div or 0.2 sec/div.
(b) Erase Program: full, Auto Erase: off
2. Swing the 10-turn, 3.5-cm diameter coil through a static magnetic
field area with B ~ 100 Gauss (1 Gauss = 10-4 Tesla) in about 10 ms,
what is the peak voltage do you expect to see based on equation (1).
Estimated peak voltage: ___________________________________
3. Use the Bell 615 Gaussmeter to measure the static magnetic field in
the gap center generated by a magnet.
Measured field: _____________
4. Swing the coil through the gap of the magnet to observe the induced
voltage e(t). Sketch e(t) below, giving vertical and horizontal scales.
Briefly explain the observed waveform.
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5. How does the waveform change as you vary the speed that you swing
the coil through the magnet?
Quantitative Measurements
A
1. A schematic of the apparatus is shown above. Make sure that the
solenoid current is off. Insert the multiturn Faraday measurement coil
into the center of the solenoid. Connect the coil to the electronic
integrator input. Connect the integrator output to the digital voltmeter,
set to the 1 volt scale. Turn the integrator on and zero it. Adjust the
potentiometer on the integrator to obtain the smallest drift in the
voltage possible. Rezero the integrator when necessary. Then turn up
the solenoid current to 10 amperes. Measure the voltage reading on
the voltmeter: Vout = _____________V.
2. Knowing the following parameters:
Resistance and capacitance inside the intergrator: R = 18kΩ , C = 0.2µF
Number of turns on the solenoid: 157 turns
Diameter of the cross-section of the solenoid: D=5 cm
Use equation (4), find the magnetic field B in the center of the solenoid.
B = _________________
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3. Using the Bell 615, Hall Effect Gaussmeter, measure the axial
magnetic induction B(z) in the solenoid for a solenoid current of 10
amperes. Compare the measured magnetic field using Gaussmeter in
the center of the solenoid with the measured value obtained from
Faraday's law in the previous step. Use B = µ 0 nI (from Biot-Savart
law) to calculate the magnetic field generated in the center of an
infinite long solenoid (Text p.235), where n is number of turns per
unit length, n = 299 turns/m for the solenoid used in this lab. Also
compare this value with your measurement using Faraday’s law.
Faraday's law measured__________________
Bell Gaussmeter measured________________
Biot-Savart law calculated_________________
4. From your measurements, estimate the external inductance L of the
solenoid using (Text p.239):
L=
N
B ⋅ ds
I ∫s
L = ________________
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