Alexander Fufaev

Formula: Helmholtz Coil (Same Current Direction)

Helmholtz Coil with Dimensions

Magnetic flux density (B-field)

Unit
Magnetic field along the symmetry axis (here along the \(z\) coordinate). For the magnetic field between the coils to be reasonably homogeneous, the distance \(d\) and the radius \(R\) must be equal.

Field point

Unit
Spatial coordinate \(z\) indicates the location where the magnetic field \(B(z)\) is present.

Distance

Unit
Distance between both coils.

Electric current

Unit
Electric current along a Helmholtz coil. The current in both coils is equal in magnitude. For this formula to work, the current in both coils must circle in the same direction.

Number of turns

Unit
Coil windings. With \(N\) windings, the current goes \(N\) times along the coil.

Vacuum permeability

Unit
The vacuum permeability is a physical constant and has the following experimentally determined value: $$ \mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}} $$