Ampère's Force Law/SI Units

Theorem
In SI units, Ampère's Force Law is expressed as:


 * $\ds \mathbf F = \dfrac {\mu_0} {4 \pi} I_1 I_2 \oint_{s_1} \oint_{s_2} \rd \mathbf l_1 \times \paren {\dfrac {\d \mathbf l_2 \times \paren {\mathbf r_1 - \mathbf r_2} } {\size {\mathbf r_1 - \mathbf r_2}^3} }$

where:
 * $\mathbf F$ is expressed in newtons
 * $\mathbf r_1 - \mathbf r_2$ is expressed in metres
 * $I_1$ and $I_2$ are expressed in amperes
 * $\mu_0$ denotes the vacuum permeability whose value is given by:
 * $\mu_0 = 1 \cdotp 25663 \, 70621 \, 2 (19) \times 10^{-6}$ henries per metre.