3B Scientific Helmholtz Coils, 300 mm - Manual (Page 2)

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3. Theoretical bases
The special arrangement of the coils is attributed to
the physicist Hermann von Helmholtz. Two narrow
coils with a large radius R are set up parallel to one
another and on the same axis so that they are also
separated by a distance R. The magnetic field of each
individual coil is non-uniform. Upon superimposition
of the two fields, a region with a magnetic field that
is largely uniform is created between the two coils.
Given the Helmholtz arrangement of the pair of coils
and coil current I, the following holds true for the
magnetic flux density B of the magnetic field:
R
n
I B
⋅ ⋅ µ ⋅ 





=
0
2
3
5
4
where n = number of turns in each coil, R = mean
coil radius and
µ
0
= magnetic field constant.
For the Helmholtz pair of coils, we get:
I . B
⋅ ⋅ = −4
10 433 7 in Tesla (I in A).
Fig. 1 Coils in Helmholtz arrangement
4. Sample experiments
In order to perform the experiments,the following
equipment is also required:
1 AC/DC power supply 0-20 V, 5 A U8521131
2 Escola 10 multimeter U8531160
1 Rotating frame with flat coil U8481510
4.1 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 middle of the
uniform field produced by the Helmholtz 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.
4.2. 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).
• When the induced current is 0, then the mag-
netic field in the coils is of the same magnitude
as the Earth’s magnetic field.