Helmholtz coils
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Objective
The objective of this experiment is to study field homogeneity of a Helmholtz coil pair.
Over the course of the preparation, the actual experiment and the writing of the report, you will gain basic knowledge on how to conduct experimental measurements. This
includes how to determine error sources and how to take them into account in your measurement. You will also learn how to design an experiment in order to verify theoretical
models.
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Experimental Equipment
Your task is to design an experimental setup with the following equipment to study the
field uniformity of Helmholz coil pair.
Never switch on the equipment without the assistants explicit authorization!
The available equipment and description of the basic functions is listed below (in
random order):
• Pair of Helmholtz coils shown in fig. 1.
Figure 1: Helmholtz coil pair.
• 2 meter 15-pole extension cord depicted in figure 2.
Figure 2: 2 meter 15-pole extention cord.
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• Power supply with continuously adjustable output between 0V and 24V or 0A and
2A (see figure 3). You can adjust either set voltage or current. The applied voltage
and current are displayed on the device.
Figure 3: Power supply.
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• Optical bench (see figure 4). It is 75 cm long and has a scale on it.
Figure 4: Optical bench
• One red (50 cm) and two blue cables (100cm) for electrical connections (an example
of a red cable is shown in figure 5).
Figure 5: Red cable.
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• Universal measuring instrument (figure 6). In combination with the correct sensor,
many different physical quantities, such as force, acceleration, magnetic flux density,
pressure or temperature can be measured. The sensors are automatically detected.
Figure 6: Universal measuring instrument.
• 2 clamping arms depicted in figure 7. They allow to connect rods or bars at 90◦
angle.
Figure 7: Clamping arm.
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• A Hall effect probe depicted in figure 8. This device includes a hall sensor allowing
measurements along the axis of the probe. Measuring ranges: ±10/±30/±100/±300/±1000
mT. Measurement error: ±2% plus 0.5% of the range limit value
Figure 8: Axial Hall sensor.
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Before the experiment
Your task is to design and assemble the experimental setup according to your plan.
Therefore, you must understand what is a Helmholtz coil and what you can measure
with the equipment. Have a discussion/meeting with your group and try to answer the
following questions:
• Derivation of the field produced by a pair of Helmholtz coils starting from BiotSavart’s law. For simplicity, derive the result parallel to the symmetry axis. Hint:
First, solve the field produced by a single current loop using Biot-Savart’s law.
• Using the expression you derived, calculate numerically the field between a pair of
coils. How the field changes when the distance between the coils is varied?
• Your design of the experimental setup. How will you assemble it? How can you
study the field? What will you measure? It’s advisable to make a sketch of your
setup.
• What are the error sources?
A simple question-answer format is enough. It is also advisable to prepare and print
excel tables to write down your results.
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During the experiment
When you arrive to the session, present your design of the experimental setup to the
assistant and explain your measurement plan. The assistant will check your plan and you
will have time to assemble it yourselves. After you are finished, ask the assistant check
your setup. Never switch on the equipment without the assistants authorization.
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The maximum current through the coils is 2 A. You cannot exceed this with the
available equipment. However, avoid applying high currents for longer periods of
time and set the current to zero when you are not measuring.
Write detailed notes of the values you measure.After you have completed the experiment, ask the assistant to check that you have performed the necessary measurements.
This is a good time to ask questions.
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After the experiment
After the experiment you should write a report of 7 (excluding title page and references) pages where you describe the experiment and present your results. Introduce the
theoretical background, and show the derivation of the expressions you obtained from
Biot-Savart’s law and the corresponding error calculations briefly.
The report should include:
• Derivation of the magnetic field of a Helmholtz coils starting from Biot-Savart’s law.
Calculate the field between the coils at the central axis of the system.
• The experimental setup. Describe the setup and the experimental procedure. What
did you measure and why?
• Compare the measured and calculated magnetic fields. Try to present your results
in a compact and informative way.
• How can you take the error in measurements into account?
Additionally, include a short essay (∼one page) on magnetic bottles covering the
following points:
• What is a magnetic bottle and how does it relate to Helmholtz coils? (Note that
you will probably create one during the experiment.)
• How does a magnetic bottle work?
• What are magnetic bottles used for?
• What does the mechanism have to with auroras (northern/polar lights)?
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