# Maxwell coil

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 $\sqrt{\frac{4}{7}}R$, and distance $\sqrt{\frac{3}{7}}R$ from the plane of
the central coil of radius $R$.
The number of ampere-turns of each of the smaller coils should equal exactly $\frac{49}{64}$ 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.

## References

1. ^ Garrett, Milan Wayne, Journal of Applied Physics, 38(6), pp2563-2586
2. ^ Clerk-Maxwell, James (1873). Treatise on Electricity and Magnetism. Oxford: The Clarendon Press. ISBN 0-486-60636-8. Page 319.
3. ^ R. Pascone, Manhattan College, T. Vullo and P.T. Cahill (1993) Theoretical and experimental analysis of magnetic field gradients for MRI from IEEE Explore