What’s all this Helmholtz coil stuff?

The Helmholtz coil was not devised to create a magnetic field, but to cancel it. The Helmholtz coil actually consists of two identical circular air-core coils, large enough to contain the work under study. The coils are situated along a common axis that extends through the experimental area. The distance between the coils is equal to their radii. They are wired in series with equal numbers of turns and the same gauge wire. Normally the voltages on them and currents flowing through them are identical and the magnetic fields are equal.

Because of the sizing and placement of the coils and the equal current flowing through them, the instrument produces within the constrained volume a region of nearly uniform, unmoving magnetic field, which is functionally equivalent to no field at all. Thus, Helmholtz coils can be used in conjunction with scientific instruments to cancel external magnetic fields, including, above all, earth’s magnetic field, which otherwise would influence the experimental outcome.

One application is to place the dual coils around a magnetometer to measure the sensitivity of an enclosed instrument. Associated with the Helmholtz coil in a typical modern outfit is an operating panel with a precision meter, reversing switch, and fine and coarse regulating dials. Current flowing through the coil causes deflections which are observed and measured through an associated microscope. Because of the uniform nature of the magnetic field, the Helmholtz coil can be used in any orientation

from vertical to horizontal.

In view of these and other exacting requirements, you might wonder how Helmholtz came to develop his precise dimensions. In reality, it is quite simple. After the overall size is determined, based on the maximum size of equipment to be studied, the coils are wound and fastened to a base. They are placed at a distance equal to the radius of the coils.

A DC source such as the Tektronix PWS 4000 DC power supply can be connected to the two series-connected coils. The unvarying applicability of Kirchhoff’s Current Law and Faraday’s Laws of Induction regulate the Helmholtz Coil.

All Helmholtz coils are defined by the relationship that the coil radius is equal to the separation distance between the two coils. These figures can vary according to the size of the apparatus under study, which must fit inside the coils. The radius/separation relationship is what keeps the magnetic field between the coils uniform. If the separation between the coils exceeds the radius, for example, the field strength between the coils is likely to exhibit two maximums and a minimum.

To produce a region with a magnetic field closer to zero, a Helmholtz coil can be calibrated to cancel out the earth’s magnetic field. (It should be noted that this

field varies with latitude since the earth flattens at the poles and is slightly weaker at higher altitudes. Also, it varies with solar eruptions.)

Helmholtz coils generally operate using a dc power source. Some applications and experimental setups, however, require an oscillating magnetic field. Examples are field susceptibility tests, precision scientific experiments and biomedical studies, notably involving living tissue. The fields may be pulsed or sinewave. Frequency can vary anywhere from 0 Hz to days or weeks, into the megawatt range and beyond. The required ac coil driver must be able to output high oscillating current to produce the higher magnetic field.