Planck charge

In physics, the Planck charge (q_P), is one of the base units in the system of natural units called Planck units. It is a quantity of electric charge defined in terms of fundamental physical constants.

The Planck charge is defined as:

$q_P = \sqrt{4 \pi\epsilon_0 \hbar c} = \sqrt{2 c h \epsilon_0} = \frac{e}{\sqrt{\alpha}} = 1.8755459 \times 10^{-18}$ coulombs,

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 constant,

$\epsilon_0 \$ is the permittivity of free space

$e \$ is the elementary charge

$\alpha \$ = (137.03599911)⁻¹ is the fine structure constant.

The Planck charge is $\alpha^{-1/2} \approx 11.706$ times greater than the elementary charge e carried by an electron.

The Gaussian cgs units are defined so that $4 \pi\epsilon_0 = 1$, in which case q_P has the following simple form:

$q_P = \sqrt{ \hbar c}.$

See also

• Orders of magnitude (charge)