Planck charge

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In physics, the Planck charge, denoted by , 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]



is the speed of light in the vacuum
is the reduced Planck constant
is the permittivity of free space
is the elementary charge
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:

Or, to put it in different words, the energy required to pile up one Planck charge within a sphere of one Planck length in diameter will make the sphere one Planck mass heavier:


is the Planck energy
is the Coulomb constant
is the Planck charge
is the Planck length
is the Planck mass

The Gaussian cgs units are defined so that , in which case has the following simple form,

It is customary in theoretical physics to adopt the Lorentz–Heaviside units (also known as rationalized cgs). When made natural (, ), they are like the SI system with . Therefore, it is more appropriate to instead define the Planck charge as


When charges are measured in units of , which is commonly used in quantum field theory, we have


See also[edit]

Notes and references[edit]

  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