Maxwell's Equations in Vacuum

We assume a working knowledge of Maxwell's equations. Their form in vacuum will be sufficient for our purposes:

$$\vec{\nabla}\cdot\vec{E} = 4\pi k_1 \rho ,$$ (2.2)

where

$$k_1 = \left\{ \begin{array}{cl} \frac{1}{4\pi\varepsilon_0} ... ...\pi} & \textrm{Heaviside-Lorentz system.} \end{array} \right.$$ (2.3)

$$\vec{\nabla}\cdot\vec{B} = 0 .$$ (2.4)

$$\vec{\nabla}\times\vec{E} = -\frac{k_2}{c} \frac{\partial\vec{B}}{\partial t} ,$$ (2.5)

where

$$k_2 = \left\{ \begin{array}{cl} c & \textrm{MKSA system,} \\... ...\\ c & \textrm{Heaviside-Lorentz system.} \end{array} \right.$$ (2.6)

$$k_2\vec{\nabla}\times\vec{B} = \frac{4\pi k_1}{c}\vec{j} + \frac{1}{c}\frac{\partial\vec{E}}{\partial t} .$$ (2.7)

For Maxwell's equations, the Heaviside-Lorentz system of units is the simplest to work with, since all factors of $4\pi$ vanish.