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3. Theoretical bases
The flat coil is rotated in an external magnetic field
so that the induced voltage can be measured at the
coil ends.
In order to accurately measure the induced voltage,
it is necessary to know the variables, on which the
induced voltage depends. These are the strength of
the external magnetic field, the speed with which it
crosses the magnetic field lines and the charge on
the charged particles that are passing through the
magnetic field. These 3 variables are related to each
other by the expression for the so-called "Lorentz
force":
r
r
r
=
⋅
×
F
q
v
B
This force acts in a direction perpendicular to both
the field B and the direction of movement of the
charged particles.
Due to the shape of the coil and the characteristics
of the medium in which the charged particles move,
an induced voltage arises at the end of the copper
loop, the magnitude of which is multiplied by the
number of turns in the coil so that it can be meas-
ured with a normal meter.
In order to create a uniform motion, the rotating
coil is connected to a slowly rotating motor. A mag-
netic field that is uniform in strength and direction
over a large volume is space is created external to
the coil by the Helmholtz coil set-up.
The charge carriers are the free electrons that move
within the copper coil. Their charge is also constant.
The rotation of the coil in the field generates a sinu-
soidal alternating voltage:
=
⋅
ω
U
U
sin
t
where
m
ω 2
=
π ⋅
f ⋅
n = Number of turns in the coil
B = Magnetic flux
A = Surface area of coil
f = Frequency of rotation of the coil within the field
A and n can be determined directly. B can be de-
termined indirectly from the Helmholtz arrange-
ment. The coil's frequency of rotation f can be ad-
justed by changing the speed of the motor and can
be measured using a photocell light barrier.
The induced voltage can be determined using an
oscilloscope or a voltmeter with its zero point cali-
brated in the centre of the dial.
For very slow rotations of the flat coil, a measure-
ment amplifier may be necessary.
4. Operation
•
Screw the supports of the rotating frame with
the flat coil to the crossbar of the Helmholtz
coils, so that the flat coil can rotate in the mid-
=
⋅
⋅
⋅
ω
U
n
A
B
and
m
dle of the uniform field produced by the Helm-
holtz coils.
•
First, conduct a preliminary experiment, turning
the coil by hand in order to estimate the level of
the induced voltage.
•
Then make a loop of string to connect the pul-
ley to the motor.
•
Conduct the subsequent experiments using this
arrangement.
5. Sample experiments
In order to perform the experiments,the following
equipment is also required:
1 AC/DC power supply 0-20 V, 5 A
2 Escola 10 multimeter
1 Pair of Helmholtz coils
5.1 Voltage induction in a magnetic field
•
Position the Helmholtz coils on the table top
and connect them in series to the DC power
supply via an ammeter.
•
Screw the supports of the rotating frame with
the flat coil to the crossbar of the Helmholtz
coils, so that the flat coil can rotate in the mid-
dle of the uniform field produced by the Helm-
holtz coils.
•
Connect a voltmeter with a central zero point
directly across the coil.
•
Set the power supply current for the coils to
about 1.5 A.
•
Use the hand crank and observe the deflection
of the voltmeter.
•
Change the speed of rotation so that a larger
deflection is obtained. The rotation speed needs
to be low.
In order to achieve a constant speed of rotation, use
of a slowly rotating motor (e.g. 12 V DC motor
U8552330) is recommended for driving the rotating
frame.
A precise voltage trace can also be observed and
measured using an oscilloscope.
5.2. Determination of the earth's magnetic field
from the induction voltage
Using the same experiment set-up, it is also possible
to measure the earth's magnetic field.
•
Align the Helmholtz coils in such a way that the
magnetic field of the coils is parallel to the
Earth's field.
•
Rotate the flat coil and observe the voltage.
•
Increase current to the Helmholtz coils until the
voltage induced at the outputs of the flat coil is
zero (so that the earth's magnetic field and the
field of the Helmholtz coils cancel out).
2
U8521131
U8531160
U8481500
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