Planck charge

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:^[1]^[2]

q_{\text{P}}={\sqrt {4\pi \epsilon _{0}\hbar c}}={\frac {e}{\sqrt {\alpha }}}\approx 1.875\;5459\times 10^{-18}

coulombs,

where

c\

is the speed of light in the vacuum

\hbar

is the reduced Planck constant

\epsilon _{0}\

is the permittivity of free space

e \

is the elementary charge

\alpha \

is the fine structure constant.

From a classical calculation,^[3] the electric potential energy of one Planck charge on the surface of a sphere that is one Planck length in diameter is one Planck energy.

The Gaussian cgs units are defined so that $4\pi \epsilon _{0}=1$ , in which case $q_{{\text{P}}}$ has the following simple form,

q_{{\text{P}}}={\sqrt {\hbar c}}.

It is customary in theoretical physics to adopt the Lorentz–Heaviside units (also known as rationalized cgs). When made natural ( $\hbar = 1$ , $c=1$ ), they are like the SI system with $\epsilon _{0}=\mu _{0}=1$ . Therefore, it is more appropriate to instead define the Planck charge as

q'_{\text{P}}={\sqrt {\epsilon _{0}\hbar c}}={\frac {e}{\sqrt {4\pi \alpha }}}\approx 5.291\times 10^{-19}

coulombs.

When charges are measured in units of $q'_{{\text{P}}}$ , which is commonly used in quantum field theory, we have

e\approx 0.30282212088~q_{\text{P}}'

.

Notes and references

↑ Stock, Michael; Witt, Thomas J (2006). "CPEM 2006 round table discussion 'Proposed changes to the SI'". Metrologia. 43 (6): 583. Bibcode:2006Metro..43..583S. doi:10.1088/0026-1394/43/6/014.
↑ Pavšič, Matej (2001). The Landscape of Theoretical Physics: A Global View. Dordrecht: Kluwer Academic. pp. 347–352. ISBN 0-7923-7006-6.
↑ The Feynman Lectures on Physics, Volume II, ch. 8: Electrostatic Energy

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[1] Stock, Michael; Witt, Thomas J (2006). "CPEM 2006 round table discussion 'Proposed changes to the SI'". Metrologia. 43 (6): 583. Bibcode:2006Metro..43..583S. doi:10.1088/0026-1394/43/6/014.

[2] Pavšič, Matej (2001). The Landscape of Theoretical Physics: A Global View. Dordrecht: Kluwer Academic. pp. 347–352. ISBN 0-7923-7006-6.

[3] The Feynman Lectures on Physics, Volume II, ch. 8: Electrostatic Energy

Planck's natural units
Planck constant Planck units
Base Planck units	Planck time Planck length Planck mass Planck charge Planck temperature
Derived Planck units	Planck energy Planck force Planck power Planck density Planck angular frequency Planck pressure Planck current Planck voltage Planck impedance Planck momentum Planck area Planck volume Planck acceleration Planck angle

Planck charge

See also

Notes and references