We have to calculate (a) the energy density of the electric field at a distance r from an electron (presumed to be a particle) at rest. (b) We will assume that the electron is not a point but a sphere of radius R over whose surface the electron charge is uniformly distributed. We will determine the energy associated with the external electric field in vacuum of the electron as a function of R. (c) We will now associate this energy with the mass of the electron, using , and calculate the value for R. We will evaluate this radius numerically; it is often called the classical radius of the electron.

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Assuming that electron is a charged sphere of radius R over whose surface charge e is uniformly distributed, electric field for will be

.

Therefore, energy density of the electric field in the space outside the electron will be

Therefore, the total energy associated with an electron of radius R and charge e will be

We now associate this energy with the mass of the electron. That is

Or

which is called the classical radius of the electron.

We next calculate its numerical value