Formula: Helmholtz Coil (Same Current Direction) Magnetic flux density (B-field)    Electric current    Number of turns   

Formula: Helmholtz Coil (Same Current Direction)
Helmholtz Coil with Dimensions
B-Field of a Helmholtz Coil along the Symmetry Axis (Same Current Direction) - Graph

Magnetic flux density (B-field)

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

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


Distance between both coils.

Electric current

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

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

Vacuum permeability

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

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