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 , and distance from the plane of
the central coil of radius .
The number of ampere-turns of each of the smaller coils should equal exactly 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.
Gradient-field Maxwell coil
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. 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. A Maxwell coil of this type is similar to a Helmholtz coil with the coil distance increased from coil radius to and the coils fed with opposite currents.
- Garrett, Milan Wayne. "Thick Cylindrical Coil Systems for Strong Magnetic Fields with Field or Gradient Homogeneities of the 6th to 20th Order". Journal of Applied Physics. 38 (6): 2563–2586. Bibcode:1967JAP....38.2563G. doi:10.1063/1.1709950.
- Clerk-Maxwell, James (1873). Treatise on Electricity and Magnetism. 2. Oxford: The Clarendon Press. p. 319. ISBN 0-486-60636-8.
- R. Pascone, Manhattan College, T. Vullo and P.T. Cahill (1993) Theoretical and experimental analysis of magnetic field gradients for MRI from IEEE Explore
- Clerk-Maxwell, James (1873). Treatise on Electricity and Magnetism. 2. Oxford: The Clarendon Press. p. 333. ISBN 0-486-60636-8.