# Ampère force law, action, reaction

by lalbatros
Tags: action, ampere, force, reaction
 P: 1,235 This is apparently a well known topic, but I did not know it before today. Let us consider the Ampère law for the force experience by a current element (1) in the magnetic fields of another current elment (2): $$\mathbf{dF}_{12} = \frac {\mu_0} {4 \pi} I_1 I_2 \frac {d \mathbf{s_2}\ \mathbf{ \times} \ (d \mathbf{s_1} \ \mathbf{ \times } \ \hat{\mathbf{r}}_{12} )} {r_{12}^2}$$ You can easily check that the "action and reaction" are not balanced by the Ampère law since: $$\mathbf{dF}_{12} + \mathbf{dF}_{21} <> 0$$ How should we understand that?