= Solution
For <rest mass> $m$ and <electric charge> $q$, the generally covariant <Lorentz force law> is
$$
\boxed{m\frac{Du^a}{d\tau}
=m\left(\frac{du^a}{d\tau}+\Gamma^a{}_{bc}u^bu^c\right)
=qF^a{}_b u^b,\qquad u^a=\frac{dx^a}{d\tau}.}
$$
Here $F_{ab}=\partial_aA_b-\partial_bA_a$ is the <electromagnetic field tensor> for the chosen <electromagnetic four-potential> normalization, and the <covariant derivative> includes the spacetime <Levi-Civita connection>. Antisymmetry of $F_{ab}$ ensures $u_aDu^a/d\tau=0$, preserving the <four-velocity> norm and the particle's <rest mass>. An uncharged particle follows a <geodesic>.
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