# Formula Lorentz force between two current-carrying wires Magnetic force Electric current Length Distance

## Magnetic force

`\( \class{green}{F} \)`Unit

`\( \mathrm{N} \)`

The magnetic part of the Lorentz force acts on a current-carrying wire because it is in the magnetic field generated by the other current-carrying wire.

Parallel, thin wires experience an equal force. Depending on the direction of the electric current, the force is either *repulsive* or *attractive*.

## Electric current

`\( \class{blue}{I_1} \)`Unit

`\( \mathrm{A} \)`

Charge per unit time flowing through the first wire.

## Electric current

`\( \class{blue}{I_2} \)`Unit

`\( \mathrm{A} \)`

Charge per unit time flowing through the second wire.

## Length

`\( L \)`Unit

`\( \mathrm{m} \)`

The longer the wire, the larger is the Lorentz force on this conductor. Here it is assumed that the two wires are

*equal in length*!## Distance

`\( r \)`Unit

`\( \mathrm{m} \)`

Distance between the two parallel wires.

## Magnetic field constant

`\( \mu_0 \)`Unit

`\( \frac{\mathrm{Vs}}{\mathrm{Am}} \)`

Magnetic field constant is a natural constant and has the exact following value:

`$$ \mu_0 ~=~ 4\pi \cdot 10^{-7} \, \frac{ \mathrm{N} }{ \mathrm{A}^2 } $$`## Number Pi

`\( \pi \)`Unit

`\( - \)`

Number Pi is a mathematical constant and has the value \( \pi ~=~ 3.1415926... \).