Download Lab 6 Magnetic Fields

Lab 6 Magnetic Fields
Introduction
We will examine and compare the magnetic fields produced by a bar magnet (permanent magnet)
and a solenoid (electromagnet).
Equipment
Power supply, DMM, rheostat, solenoid, magnetic field sensor, bar magnet, ruler and meter stick.
Background
All magnets, whether permanent or electromagnetic, have two poles. Magnetic fields radiate from
one pole then bends around to the other. The magnitude of the magnetic field decreases as the
distance from the magnet increases.
For the bar magnet, we can measure only the magnetic field outside it, for a solenoid, we can
actually measure the magnetic field inside it. We will observer the magnetic field behavior of both
along the axis of the magnets.
The magnetic field along the axis of the permanent magnet points along the axis and is inversely
proportional to the distance from the magnet cubed at locations “far” from the magnet.
permanent
magnet
S
N
∝
B(r) 1/r3
solenoid
currents
The strength of the magnet that produces a magnetic field is characterized by the magnetic
moment of the magnet, M.
B(r)permanent magnet =
µoM 1
2π r 3
The same generalization holds true for the solenoid but the strength is characterized by the
current, I, and the number of windings per unit length, n.
B(r)outside solenoid =
µonI 1
2 r3
Moreover, the magnetic field inside the solenoid is constant.
Binside solenoid = µonI
The permeability of free space, µo, is 4π x 10-7 T•m/A.
Experiment: Set Up
Set the magnetic field sensor to the “axial” setting. This tells the magnetic field sensor to measure
only the component of the magnetic field along the length of the sensor. Connect the magnetic
field sensor to channel A of the interface box. Display a readout of magnetic field. Under the
“setup” tab, set the multiplier to “1x” and unit to “gauss” (10-4 T), and set the sample rate to 1 Hz.
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Be sure to click on the “tare” button on the sensor before every set of measurement while the
sensor is away from any magnetic field source and shielded. This is to tell the sensor to ignore
the magnetic field due to ambient sources such as the Earth and nearby furniture.
Experiment: Bar Magnetic Field
Place the edge of the magnetic field sensor 4 cm from either end of the bar magnet. If possible,
use two bar magnets stacked together with the same poles at the same end.
4 cm
S
magnetic field
sensor
x
N
Measure the magnetic field strength as a function of the distance from the edge of the magnet 1
cm at a time until the magnetic field reading dips below 1x10-5 T. Plot the ln(B) on the y axis and
ln(r) on the x axis. Find the slope of this line. Compare it to the slope that it is supposed to be, –
3.
⎛µ
⎞1
B = ⎜⎜ o M ⎟⎟⎟ 3
⎜⎝ 2π ⎟⎠ r
⇒
⎛µ
⎞
ln B = ln ⎜⎜ o M ⎟⎟⎟ − 3 ln r
⎜⎝ 2π ⎟⎠
⎛µ
⎞
⇒ Y = ln ⎜⎜ o M ⎟⎟⎟ − 3X
⎜⎝ 2π ⎟⎠
a. What is the percent difference between the measured value and the expected value of –3?
b. Use the y-intercept to find the magnetic moment of the magnet, M. The unit of the magnetic
moment is A•m2.
Experiment: Solenoid
Build the following circuit. Connect the solenoid to the rheostat (a high-current, variable resistor),
the power supply, and the DMM (connected and set to measure current to the “A” range) in series.
power
supply
–
+
slider
solenoid
rheostat/resistor
DMM
(set to A)
Before turning on the power supply, shield and tare the magnetic field sensor. Turn on the power
supply and set it to about 20 V. Adjust the rheostat until the current reads about 1 A. Monitor the
rheostat temperature to make sure it doesn't get too hot.
First, measure the magnetic field sensor inside the solenoid.
solenoid
magnetic field sensor
a. What is the percent difference between the measured value and the expected value found
from the following equation?
B = µonI
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Second, measure the magnetic field strength as a function of the distance from the edge of the
solenoid 1 cm at a time until the magnetic field reading dips below 1x10-5 T. Start the data
collection and move the magnetic field sensor 1 cm at a time until the magnetic field reading dips
below 1x10-5 T.
4 cm
magnetic field
sensor
solenoid
x
Plot the ln(B) on the y axis and ln(r) on the x axis. Find the slope of this line. Compare it to the
slope that it is supposed to be, –3.
⎛µ
⎞1
B = ⎜⎜ o πnI ⎟⎟⎟ 3
⎜⎝ 2π
⎟⎠ r
⇒
⎛µ
⎞
ln B = ln ⎜⎜ o πnI ⎟⎟⎟ − 3 ln r
⎜⎝ 2π
⎟⎠
⎛µ
⎞
⇒ Y = ⎜⎜ o πnI ⎟⎟⎟ − 3X
⎜⎝ 2π
⎟⎠
a. What is the percent difference between the measured value and the expected value of –3?
b. Use the y-intercept to find the equivalent magnetic moment of the magnet. It is this.
M = πnI
c. Which object has a larger magnetic moment, the bar magnet or the solenoid?
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