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:
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.