# Lorentz–Heaviside units

Lorentz–Heaviside units

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 $sqrt \left\{4 pi\right\}$ 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.

Maxwell's equations with sources

The equations with sources take the following form:

:$abla cdot mathbf\left\{E\right\} = ho$

:$abla cdot mathbf\left\{B\right\} = 0$

:$abla imes mathbf\left\{E\right\} = -frac\left\{1\right\}\left\{c\right\} frac\left\{partial mathbf\left\{B \left\{partial t\right\}$

:$abla imes mathbf\left\{B\right\} = frac\left\{1\right\}\left\{c\right\} frac\left\{ partial mathbf\left\{E \left\{partial t\right\} + frac\left\{1\right\}\left\{c\right\} mathbf\left\{J\right\}$

where "c" is the speed of light in a vacuum. Here E is the electric field, B is the magnetic field, $ho$ 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

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

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

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

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:

: $mathbf\left\{F\right\} = q \left(mathbf\left\{E\right\} + frac\left\{mathbf\left\{v\left\{c\right\} imes mathbf\left\{B\right\}\right),$

where q is the charge on the particle and v is the particle velocity. The magnetic field B has the same units as the electric field E.

* [http://www.du.edu/~jcalvert/phys/hlu.htm Heaviside–Lorentz units]

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