Planck charge


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 the only base Planck unit that does not depend on the gravitational constant and is defined as:
where
From a classical calculation, 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 accumulate one Planck charge on a sphere one Planck length in diameter will make the sphere one Planck mass heavier:
where
If instead, a rationalized form of Planck units is chosen, in which units are defined in terms of, and without numeric factors, the resulting rationalized Planck charge is
When charges are measured in units of, which is commonly used in quantum field theory, we have

Physical significance

The Planck charge is the maximum amount of charge that a black hole the size of one Planck length can possess, and adding more charge would make the black hole inevitably larger. In particular, Reissner–Nordström metric tends to the Planck length for a mass that tends to zero and a charge that equals the Planck charge.