Chapter 1

Electrostatics and Magnetostatics

Electrostatic energy of an electron

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An electron is considered as a sphere of radius in which the charge is evenly distributed, with the density .

We additionally suppose all the energy is in an electrostatic form.

We give :

and (electron's mass).

Question

Compute the electrostatic energy of the electron.

Deduce an order of magnitude of .

Hint

Imagine the electron is like an onion. It was built by bringing thin spherical and concentric layers from the infinity ...

Solution

Let's establish the expression of the electrostatic energy of a sphere of radius .

It is evenly charged in volume, has total charge , and a density of charges .

Let's build this sphere in a reversible manner. We bring the charge , from the infinity.

Its potential increases from zero to the potential of the sphere, under construction, of radius , given by :

The elementary work required is :

Hence :

To get an order of magnitude of , we must identify the electrostatic energy calculated to the energy of mass given by Einstein's relativity :

So :

Remarque

By analogy, the gravitational energy of a star (or planet) of mass and radius can be deduced :

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