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.

The Planck charge is times larger than the elementary charge e carried by an electron. A Planck charge concentrated within a Planck length possesses an electric potential energy that equals (converted to mass) one Planck mass.

As an example, packing together twelve electrons (11.706 is a fractional number and cannot be used) will make them weigh 2.287×10−8 kg, slightly more than the Planck mass (2.176×10−8 kg), and roughly the mass of a flea egg, solely by virtue of their electric potential energy. Note that the rest mass of the electron alone is 9.109×10−31 kg, or 23 orders of magnitude smaller.

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 (ħ=1, c=1), 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 , i.e., when is set equal to 1, we obtain

which is commonly used in quantum field theory, so that e≅0.30282212088.

By contrast, in (non-rationalized) natural cgs units where 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.