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]
\begin{equation}
\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}
\end{equation}
\begin{equation}
c\mathbf{B}=\mathbf{e}_{r^{\prime}}\boldsymbol{\times}\mathbf{E}
\nonumber
\end{equation}
[\math]