# Classical Electromagnetics - Feynman's Equation

Author:
diracpaul
In this Section we'll prove an important equation that Feynman gives in his Lectures without proof. In his own words: When we studied light, we began by writing down equations for the electric and magnetic fields produced by a charge which moves in any arbitrary way. Those equations were [math] $$\mathbf{E}=\frac{q}{4\pi\epsilon_{0}}\left[\frac{\mathbf{e}_{r^{\prime}}}{r^{\prime}^{2}}+\frac{r^{\prime}}{c}\frac{d}{dt}\biggl(\frac{\mathbf{e}_{r^{\prime}}}{r^{\prime}^{2}}\biggr)+\frac{1}{c^{2}}\frac{d^{2}}{dt^{2}}\mathbf{e}_{r^{\prime}}\right] \tag{21.1}$$ $$c\mathbf{B}=\mathbf{e}_{r^{\prime}}\boldsymbol{\times}\mathbf{E} \nonumber$$ [\math]