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).
Compute the electrostatic energy of the electron.
Deduce an order of magnitude of .
Imagine the electron is like an onion. It was built by bringing thin spherical and concentric layers from the infinity ...
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 :
To get an order of magnitude of , we must identify the electrostatic energy calculated to the energy of mass given by Einstein's relativity :
By analogy, the gravitational energy of a star (or planet) of mass and radius can be deduced :