= Solution
With no electric field, the <Lorentz force> is
$$
\boxed{\mathbf F=q\mathbf v\times\mathbf B.}
$$
For nonrelativistic motion, the <work-energy theorem> gives
$$
\frac{dK}{dt}=\frac{d}{dt}\left(\frac12m|\mathbf v|^2\right)=m\dot{\mathbf v}\cdot\mathbf v=\mathbf F\cdot\mathbf v=q(\mathbf v\times\mathbf B)\cdot\mathbf v=0.
$$
Consequently $\boxed{K(t)=K(0)}$. The reason is geometric: <magnetic forces do no work> because they are perpendicular to the instantaneous <velocity>. They can change its direction but not its magnitude. The same energy conclusion holds relativistically, using $dE/dt=\mathbf F\cdot\mathbf v$ and subtracting the constant rest energy to obtain <kinetic energy>.
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