View Single Post
0xDEADBEEF
#1
Jan31-13, 06:07 PM
P: 825
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]
and
[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 Phys.org
Symphony of nanoplasmonic and optical resonators produces laser-like light emission
Do we live in a 2-D hologram? New Fermilab experiment will test the nature of the universe
Duality principle is 'safe and sound': Researchers clear up apparent violation of wave-particle duality