- 1,001

- 299

**Homework Statement**

Show that for the case of a general inhomogeneous magnetic field, $$\dot{\vec{v}}=\frac{e}{2mc} (\vec{v} \times \vec{B} - \vec{B} \times {v})$$

**The attempt at a solution**

I think I am oversimplifying things. I used that, for an electron in a magnetic field, [itex]m \frac{d \vec{v}}{dt}=e \vec{v} \times \vec{B}[/itex], and that [itex]\vec{v} \times \vec{B} = - \vec{B} \times \vec{v} [/itex]

Doing this, I find that [itex]RHS = \frac{1}{c} \dot{\vec{v}}[/itex]