Heaviside–Lorentz units

Lorentz-Heaviside units for Maxwell's equations are often used in relativistic calculations. They differ from the equations in cgs untis by a factor of $4\pi$ in the definition of electric charge.

Maxwell's equations with sources

The equations with sources take the following form:

$\nabla \cdot \mathbf {E} =\rho$

$\nabla \cdot \mathbf {B} =0$

$\nabla \times \mathbf {E} =-{\frac {1}{c}}{\frac {\partial \mathbf {B} }{\partial t}}$

$\nabla \times \mathbf {B} ={\frac {1}{c}}{\frac {\partial \mathbf {E} }{\partial t}}+{\frac {1}{c}}\mathbf {J}$

where c is the speed of light in a vacuum.

Lorentz force

The force exerted upon a charged particle by the electric field and magnetic field is given by the Lorentz force equation:

$\mathbf {F} =q(\mathbf {E} +{\frac {\mathbf {v} }{c}}\times \mathbf {B} ),$

where $q\$ is the charge on the particle and $\mathbf {v} \$ is the particle velocity. This is slightly different from the SI-unit expression above. For example, here the magnetic field $\mathbf {B} \$ has the same units as the electric field $\mathbf {E} \$.