Helmholtz coils

Helmholtz coil is a device that can produce a uniform magnetic field in a small area. The helmholtz coil is often used in physical experiments because of its open nature, which makes it easy to put or remove other instruments and make direct visual observations. Named after The German physicist Hermann von Helmholtz

A Helmholtz coil consists of a pair of identical circular conductor coils. Using a cartesian coordinate system, the central axes of the two circular coils of radius R are coaxial with the Z-axis. The z-coordinates of the two circular coils are respectively and. Each conductor coil carries a cocurrent I.
The setting minimizes the nonuniformity of the magnetic field at the center of the two coils, O (the origin). This action also means that the leading non-zero differential project is, and this argument will be explained in more detail later. However, this still leaves about a 7% difference in magnetic field values between the coil plane and the z-axis intersection and the O point.
In some applications, helmholtz coils can be used to counteract the earth's magnetic field, creating regions with a near-zero magnetic field.

It is necessary to apply Bessel function or elliptic function and related techniques to calculate the exact magnetic field at any position in space. Along the central axis of the coil (z-axis), the calculation involved is relatively simple. Taylor expansion can be applied to expand the magnetic field into a power series of. The rectangular coordinate system is adopted, and the center of helmholtz coil is taken as the origin O of z-axis. Since for symmetry in the XY - plane, the odd power must be equal to zero. By adjusting the distance between the two coils, point O can be turned into an inflection point, so grade 1 items can be guaranteed to be zero, so leading uneven items are grade 1 items.
At the central position O, the magnetic field is zero
Where, is the magnetic constant. [1]