- Lorentz–Heaviside units
**Lorentz–Heaviside**units (or**Heaviside–Lorentz**units) forMaxwell's equations are often used in relativistic calculations. They differ from the equations inCGS units by a factor of $sqrt\; \{4\; pi\}$ in the definitions of the fields andelectric charge . The units are particularly convenient when performing calculations in spatial dimensions greater than three such as is done instring theory .**Maxwell's equations with sources**The equations with sources take the following form:

:$abla\; cdot\; mathbf\{E\}\; =\; ho$

:$abla\; cdot\; mathbf\{B\}\; =\; 0$

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

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

where "c" is the speed of light in a vacuum. Here

**E**is the electric field,**B**is the magnetic field, $ho$ 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

:$q\_\{LH\}\; stackrel\{mathrm\{def\{=\}\; sqrt\{4pi\}\; q\_\{cgs\}$

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

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

**Lorentz force**The force exerted upon a charged particle by the

electric field andmagnetic field is given in both cgs and Lorentz–Heaviside units by theLorentz force equation:: $mathbf\{F\}\; =\; q\; (mathbf\{E\}\; +\; frac\{mathbf\{v\{c\}\; imes\; mathbf\{B\}),$

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**.**External links*** [

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

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