# Maxwell coil

Magnetic field lines around a Maxwell coil
Modulus of the magnetic field around a 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.

## Description

A constant-field Maxwell coil set consists of three coils oriented on the surface of a virtual sphere.[1]
According to Maxwell's original 1873 design:[2]
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.

A gradient-field Maxwell coil is essentially the same geometry of the 3-coil configuration above, with the central coil removed to leave only the smaller two coils.[3] If the current in one of the coils is reversed, a uniform-gradient magnetic field is produced near the centre of the two coils. Maxwell describes the use of the 2-coil configuration for the generation of a uniform force on a small test coil.[4] A Maxwell coil of this type is similar to a Helmholtz coil with the coil distance increased from coil radius ${\displaystyle R}$ to ${\displaystyle {\sqrt {3}}R}$ and the coils fed with opposite currents.