= Solution
With $P^\mu=mU^\mu$, $U^\mu=dx^\mu/d\tau$, and $F^{\mu\nu}$ the field tensor, separating temporal and spatial components yields the <Lorentz force> and power equations. The invariants are $E\cdot B$ and $E^2-c^2B^2$. For perpendicular fields with $E\lt cB$, boost with $v=E\times B/B^2$ (here $-E\hat y/B$); then $E\prime=0$ and $B\prime=\sqrt{B^2-E^2/c^2}\,\hat z$. Perpendicular motion is circular with $\omega=|q|B\prime/(\gamma m)$ and radius $p/(|q|B\prime)$. Transforming back adds the frame <velocity>, giving the nonrelativistic $E\times B/B^2$ drift, independent of $m,q$; a parallel <velocity> would additionally produce a helix.
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