Force between Infinite Parallel Straight Conductors carrying Steady Current

Theorem

Let $s_1$ and $s_2$ be wires in a vacuum carrying steady currents $I_1$ and $I_2$.

Let $s_1$ and $s_2$ be parallel and (effectively) infinitely long.

Then the force between $s_1$ and $s_2$ is given by:

$\mathbf F = \dfrac {\mu_0 I_1 I_2} {2 \pi r}$

where:

$r$ denotes the distance between $s_1$ and $s_2$

$\mu_0$ denotes the vacuum permeability.

Proof

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