# 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.

## Vacuum permeability

`$$ \mu_0 $$`Unit

`$$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$`

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 \( \pi ~=~ 3.1415926... \).