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Lorentz force

For four-momentum

p^{μ}

and four-velocity

u^{μ}

, the covariant Lorentz-force law is

\frac{d p ^{μ}}{d τ} = q F^{μν} u_{ν} .

Its spatial and temporal components are

\frac{d p}{d t} = q (E + v \times B), \frac{d E}{d t} = q E \cdot v .

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