Mathjax Test

\(\LaTeX\) and MathJax test

A test of \(\LaTeX\) export to MathJax.

Maxwell-Heaviside equations:

\begin{aligned} \boldsymbol{\nabla} \boldsymbol{\cdot} \boldsymbol{E} &= \frac{\rho}{\epsilon_0} & \boldsymbol{\nabla} \boldsymbol{\cdot} \boldsymbol{B} &= 0 \\ \boldsymbol{\nabla} \times \boldsymbol{E} &= -\frac{\partial \boldsymbol{B}}{\partial t} & c^2 \boldsymbol{\nabla} \times \boldsymbol{B} &= \frac{\boldsymbol{j}}{\epsilon_0} + \frac{\partial \boldsymbol{E}}{\partial t} \\ \end{aligned}

Their solutions:

\begin{aligned} \boldsymbol{E} &= -\boldsymbol{\nabla} \phi - \frac{\partial \boldsymbol{A}}{\partial t} \\ \boldsymbol{B} &= \boldsymbol{\nabla} \times \boldsymbol{A} \\ \end{aligned} \begin{aligned} \phi(1,t) &= \int\frac{\rho(2,t-r_{12}/c)}{4\pi\epsilon_0 r_{12}}\,dV_2 \\ \boldsymbol{A}(1,t) &= \int\frac{\boldsymbol{j}(2,t-r_{12}/c)}{4\pi\epsilon_0 c^2r_{12}}\,dV_2 \end{aligned}

Maxwell would have approved of these, BUT not Heaviside who thought it was "best to murder the whole lot", i.e. the scalar and vector potentials (\(\phi\), \(\boldsymbol{A}\)).