If a particle with charge e and mass m is in an arbitrary magnetic field has motion described by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]m\frac{d^2\vec{r}}{dt^2}=\frac{e}{c}\frac{d\vec{r}}{dt}\times\vec{H} [/tex]

prove that the speed [tex]v\equiv\left\vert\frac{d\vec{r}}{dt}\right\vert[/tex] is constant.

I don't understand how to do this when the field isn't necessarily constant.

Any suggestions would be greatly appreciated. Thanks!

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# Homework Help: Differential Equation with Vector Product

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