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{c}
{wiki}

= Lorentz force law
{c}
{synonym}

For <four-momentum> $p^\mu$ and <four-velocity> $u^\mu$, the covariant Lorentz-force law is
$$
\frac{dp^\mu}{d\tau}=qF^{\mu\nu}u_\nu.
$$
Its spatial and temporal components are
$$
\frac{d\mathbf p}{dt}=q(\mathbf E+\mathbf v\times\mathbf B),
\qquad
\frac{d\mathcal E}{dt}=q\mathbf E\cdot\mathbf v.
$$

Lorentz force

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