Planck charge

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In physics, the Planck charge, denoted by qP, 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 \pi\epsilon_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 4πε0 = 1, giving qP 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.

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Planck's natural units
Base Planck units
Derived Planck units