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

## 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: $$\mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}}$$

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