Maxwell coil

A Maxwell coil is a device for producing a large volume of almost constant (or constant-gradient) magnetic field. It is named in honour of the Scottish physicist James Clerk Maxwell.

A Maxwell coil is an improvement of a Helmholtz coil: in operation it provides an even more uniform magnetic field (than a Helmholtz coil), but at the expense of more material and complexity.

A constant-field Maxwell coil set consists of three coils oriented on the surface of a virtual sphere.
According to Maxwell's original 1873 design:
each of the outer coils should be of radius ${\displaystyle {\sqrt {\frac {4}{7}}}R}$, and distance ${\displaystyle {\sqrt {\frac {3}{7}}}R}$ from the plane of
the central coil of radius ${\displaystyle R}$.
The number of ampere-turns of each of the smaller coils should equal exactly ${\displaystyle {\frac {49}{64}}}$ of the middle coil.
This arrangement removes variations in magnetic field, up to its 6th-order derivative with respect to position, near the centre of the virtual sphere.

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