Category:Ampère's Force Law

This category contains pages concerning Ampère's Force Law:

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

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

$\ds \mathbf F \propto I_1 I_2 \oint_{s_1} \oint_{s_2} \rd \mathbf l_1 \times \paren {\dfrac {\d \mathbf l_2 \times \paren {\mathbf r_1 - \mathbf r_2} } {\size {\mathbf r_1 - \mathbf r_2}^3} }$

where:

$\d \mathbf l_1$ and $\d \mathbf l_2$ are infinitesimal vectors associated with $s_1$ and $s_2$ respectively

$\mathbf r_1$ and $\mathbf r_2$ are the position vectors pointing from $\d \mathbf l_2$ towards $\d \mathbf l_1$.