= Boosted uniform line charge
{title2=$\lambda=\gamma\lambda_0,\quad I=\lambda u$}
An infinite uniform line with proper charge per unit <length> $\lambda_0$ moving axially at <speed> $u$ has Lorentz-contracted <density> $\lambda=\gamma\lambda_0$ and current $I=\lambda u$. Transverse distance $r$ is unchanged by the boost. The rest <electric field> $\lambda_0\widehat{\mathbf r}/(2\pi\epsilon_0r)$ transforms into $\mathbf E=\lambda\widehat{\mathbf r}/(2\pi\epsilon_0r)$ and $\mathbf B=\mathbf u\times\mathbf E/c^2$. This equals the <magnetic field> $\mu_0I\widehat{\boldsymbol\varphi}/(2\pi r)$ from <Ampère's law>. The formulas concern a uniform stationary current pattern, not an accelerating finite filament's radiation.
Back to article page
