Download 7. Magnetic Fields

7. Magnetic Fields
Part 1: Magnetic field of a current carrying coil
Objective To verify the formula for the magnetic field of a current-carrying circular coil
Background The magnetic field at the center of an N-turn circular coil of radius R
carrying current I is
Bc 
 0 NI
(1)
2R
Its direction is normal to the plane of the coil, and is out of the paper if the current is
counter clockwise as shown.
.B
This can be verified by measuring the magnetic field using a magnetic probe. The probe
reads the component Bn of the magnetic field B in the direction pointing out of a white
spot on it.
Bn
B
White spot
Because of the presence of ambient magnetic field, when the probe is placed at the center
of the coil, it measures the sum of the component of the ambient field Ba and the field
due to the current. The relation between the probe reading B and the current is therefore
B  Bc  Ba
(2)
A plot of B versus I is expected to be straight line.
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Procedure:
1. To familiarize your self with the magnitude of the magnetic field expected in this
experiment, measure the diameter of the coil, count the number of turns, and
calculate the magnetic field strength at the center assuming a 100mA current
running in the coil. Express your answer in µT.
2. Set up a circuit with a power supply connected in series with (a) an ammeter, (b) a
10-Ω resistor, and (c) the circular coil. Facing you, the coil should have its red
lead on the right, and the current should go in from the red lead.
3. Determine the direction of the magnetic field at the center of the coil due to the
current and place the probe at the center with the proper orientation. Set the
maximum field at 0.3mT for the probe. By fine tuning the voltage of the power
supply, set the current I at five values from 0.1A to 0.5A and record the probe
readings B in µT.
4. Plot B against I . Measure the slope of the fitted straight line, and compare it with
the value you would expect. What is the percentage error?
5. Determine the component of the ambient field Ba from the graph.
PART 2 Earth’s Magnetic Field
Objective: To measure the earth’s magnetic field
Background:
The earth’s magnetic field in the northern hemisphere points downward and makes an
angle θ with the horizontal plane called the dip angle, or declination. If Be denotes the
strength of the field, its horizontal component is given by
Bh  Be cos
(3)
Bh
θ
Be
The direction of the horizontal component can be measured using a compass. Its value
Bh can be measured with the help of the circular coil in the following manner. Arrange
the field Bc produced at the center of the coil to be perpendicular to the horizontal
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component Bh . The resulting field is the vector sum of Bc and Bh on the horizontal
plane. The direction of this resulting field can be measured with a compass. When this
direction deviates from the direction of the horizontal component of the earth’s field by
45º, we have
Bh  Bc .
(4)
Bc can be calculated if we measure the current I when this happens.
Bh
45º
Bc
Procedure
1. Set up the same circuit as in Part 1. Make sure the coil is far from any other
visible source of magnetic field.
2. Place a compass at the center of the coil. Rotate the coil so that the compass
needle lies on the plane of the coil. This ensures that the field produced by the coil
current will be perpendicular to the horizontal component of the earth’s field.
3. Adjust the voltage on the power supply so that the needle deflects by 45º from its
original position. Record the current I .
4. Calculate Bc using Eq.(1), and therefore Bh .
5. Use a magnetic needle to measure the dip angle  . (Note: the needle should be
placed far from the coil in the course of the experiment.)
6. Calculate the strength of the earth’s magnetic field Be
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