Planck charge

In physics, the Planck charge, denoted by $q\_P$, is a quantity of electric charge defined in terms of fundamental constants. It is the unit of charge in the system of natural units known as Planck units. The Planck charge is defined as

:$q\_P\; =\; sqrt\{4\; piepsilon\_0\; hbar\; c\}\; =\; sqrt\{2\; c\; h\; epsilon\_0\}\; =\; frac\{e\}\{sqrt\{alpha$

where :

:$c$ is the speed of light in the vacuum,:$h$ is Planck's constant, :$hbar\; equiv\; frac\{h\}\{2\; pi\}$ is the "reduced" Planck's constant or Dirac's constant, :$epsilon\_0$ is the permittivity of free space:$e$ is the elementary charge:$alpha$ = (137.03599911)⁻¹ is the fine structure constant.

Some systems of units (such as Gaussian cgs units) are defined so that $4\; piepsilon\_0\; =\; 1$, giving $q\_P$ the simple form:

:$q\_P\; =\; sqrt\{\; hbar\; c\}$

Its value as expressed in SI units is

:$q\_P$ = 1.8755459 × 10 ⁻¹⁸ C.

The Planck charge is approximately 11.706 times greater than the elementary or electron charge.