Planck charge

In physics, the Planck charge, denoted by formula_1, 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; it 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,
In other 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
"Rationalized units": If, instead, a rationalized form of Planck units is chosen, in which units are defined in terms of ℏ, and formula_5 without numerical factors, the resulting rationalized Planck charge is
When charges are measured in units of formula_18, used in quantum field theory, one has