Lorentz–Heaviside units

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Lorentz–Heaviside units (or Heaviside–Lorentz units) for Maxwell's equations are often used in relativistic calculations. They differ from the equations in CGS units by a factor of $\sqrt {4 \pi}$ in the definitions of the fields and electric charge. The units are particularly convenient when performing calculations in spatial dimensions greater than three such as is done in string theory.

[edit] 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. Here E is the electric field, B is the magnetic field, $ρ$ is the charge density, and J is the current density.

The charge and fields in Lorentz–Heaviside units are related to the quantities in cgs units by

$q_{LH} \ \stackrel{\mathrm{def}}{=}\ \sqrt{4\pi} q_{cgs}$

$\mathbf{E}_{LH} \ \stackrel{\mathrm{def}}{=}\ { \mathbf{E}_{cgs} \over \sqrt{4\pi} }$

$\mathbf{B}_{LH} \ \stackrel{\mathrm{def}}{=}\ { \mathbf{B}_{cgs} \over \sqrt{4\pi} }$ .

[edit] Lorentz force

The force exerted upon a charged particle by the electric field and magnetic field is given in both cgs and Lorentz–Heaviside units by the Lorentz force equation:

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