- #1
lalbatros
- 1,256
- 2
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):
[tex]\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} [/tex]
You can easily check that the "action and reaction" are not balanced by the Ampère law since:
[tex]\mathbf{dF}_{12} + \mathbf{dF}_{21} <> 0 [/tex]
How should we understand that?
Let us consider the Ampère law for the force experience by a current element (1) in the magnetic fields of another current elment (2):
[tex]\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} [/tex]
You can easily check that the "action and reaction" are not balanced by the Ampère law since:
[tex]\mathbf{dF}_{12} + \mathbf{dF}_{21} <> 0 [/tex]
How should we understand that?