= Solution
With no <electric field>, the power relation from part (a) gives
$$
\frac d{dt}(\gamma mc^2)=e\mathbf v\cdot(\mathbf v\times\mathbf B)=0.
$$
Consequently
$$
\boxed{\gamma(t)=\gamma_0,\qquad |\mathbf v(t)|=|\mathbf v_0|.}
$$
The magnetic part of the <relativistic Lorentz force> changes the direction of <mechanical momentum>, but performs no work. This conclusion does not require the <magnetic field> to be spatially uniform: it follows from the local orthogonality of $\mathbf v$ and $\mathbf v\times\mathbf B$.
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