View Single Post
0xDEADBEEF is offline
Jan31-13, 06:07 PM
P: 824
Newtons third law states that there is a counter force to every force. Unfortunately this doesn't seem to work for moving point charges. The Coulomb force cancels out but
the B-Field of a moving point charge is:
[tex]\mathbf{B}=\frac{\mu_0}{4\pi}q \frac{\mathbf{v}\times\mathbf{r}}{\left|r\right|^3}[/tex]
And the Lorenz force is
[tex]\mathbf{F}=q\, \mathbf{v}\times \mathbf{B}[/tex]

Lets assume that the two charges have velocities [itex]\mathbf{v}_1,\mathbf{v}_1[/itex]

Therefore the two Lorenz forces are
[tex]\mathbf{F}_1=k(r)\, \mathbf{v}_1 \times (\mathbf{v}_2 \times\mathbf{r}) [/tex]
[tex]\mathbf{F}_2=k(r)\, \mathbf{v}_2 \times (\mathbf{v}_1 \times (- \mathbf{r})) [/tex]
Due to the Jacobi identity the sum of the two forces is not zero
[tex]\mathbf{F}_1+\mathbf{F}_2=- k(r)\, \mathbf{r}\times(\mathbf{v}_1\times \mathbf{v}_2)[/tex]

What is the solution here? The Pointing vector? Relativity? I think that the basic formulas must be correct for slowly moving charges. So it shouldn't be due to non linear trajectories, neglected acceleration or some such thing.
Phys.Org News Partner Physics news on
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser