Jefimenko's Equations

#Physics
Describes electric and magnetic fields for retarded potentials

$\displaystyle \vec{E}(\vec{r},t)=k\int \left[ \frac{\rho(\vec{r}',t_{r})}{\mathscr{r}^{2}} \mathscr{\hat{r}}+ \frac{\dot{\rho}(\vec{r}',t_{r})}{c\mathscr{r}}\mathscr{\hat{r}}- \frac{\dot{\vec{J}}(\vec{r}',t_{r})}{c^{2}\mathscr{r}}\right] , \mathrm{d}\tau'$

$\displaystyle \vec{B}(\vec{r},t)=\frac{{\mu}{0}}{4\pi}\int \left[\frac{\vec{J}(\vec{r}',t{r})}{\mathscr{r}^{2}}+ \frac{\dot{\vec{J}}(\vec{r}',t_{r})}{c\mathscr{r}}\right] , \mathrm{d}\tau'$