Retarded Potentials

Potentials for moving charges or currents (information doesn’t travel instantaneously, so we use retarded time)

Topics

• Jefimenko’s Equations
• Lienard-Wiechert Potentials

$V(\vec{r},t)=k\int \frac{\rho ({\vec{r}}^{\prime },t_r)}{r}\mathrm{d}{\tau }^{\prime }$

• $t_r$ is the retarded time

$\vec{A}(\vec{r},t)=\frac{{\mu }_0}{4\pi }\int \frac{\vec{J}({\vec{r}}^{\prime },t_r)}{r}\mathrm{d}{\tau }^{\prime }$