The Helmholtz coil consists of two identical circular coils separated by a distance equal to the coil radius r connected so that current I through the coils will run in parallel.

The setup generates a very homogenous and straight forward to calculate magnetic field B between the coils, thus making the setup ideal for simple physical experiments.

In the center of the coil the magnetic field can be derived as:

B= &mu0*I / (r*(5/4)^(3/2))

where &mu0 is the permeability of free space. In the case not along center axis the expression becomes a bit more complex.

When one of the coils is reversed a magnetic quadropole is formed. Other variations include setups with coils two or three axes.