Specific weight

In physics, the Planck charge, denoted by $q_{\text{P}}$, 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:

$q_{\text{P}}=\sqrt{4\pi {ϵ}_0\hslash c}=\sqrt{2ch{ϵ}_0}=\frac{e}{\sqrt{\alpha }}=1.8755459\times 10^{-18}$ coulombs,

where:

$c$ is the speed of light in the vacuum,

$h$ is Planck's constant,

$\hslash \equiv \frac{h}{2\pi }$ is the reduced Planck constant,

${ϵ}_0$ 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 $4\pi {ϵ}_0=1$, in which case $q_{\text{P}}$ has the following simple form:

$q_{\text{P}}=\sqrt{\hslash c}.$

It is customary in theoretical physics to adopt the Lorentz–Heaviside units (also known as rationalized cgs). When made natural ($c=1$) they are like the SI system with ${ϵ}_0={\mu }_0=1$. Therefore it is more appropriate to define the Planck charge as

$q{\text{'}}_{\text{P}}=\sqrt{{ϵ}_0\hslash c}=\frac{e}{\sqrt{4\pi \alpha }}=5.291\times 10^{-19}$ coulombs,

When charges are measured in units of $q{\text{'}}_{\text{P}}$, i.e., when $q{\text{'}}_{\text{P}}$ is set equal to 1, we obtain $\alpha =e^2/(4\pi )$, which is commonly used in theoretical physics. In contrast, in (non-rationalized) natural cgs units where $q_{\text{P}}=1$ we have $\alpha =e^2$.

See also

• Orders of magnitude (charge)

Notes and references

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