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.

Sources

This page may be the result of a refactoring operation. As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering. If you have access to any of these works, then you are invited to review this list, and make any necessary corrections. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{SourceReview}} from the code.

• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Appendix $\text A$: Units