In a 1911 paper, Ernst Rutherford said:

“In order to form some idea of the forces required to deflect an alpha particle through a large angle, consider an atom containing a point positive charge Ze at its centre and surrounded by a distribution of negative electricity, uniformly distributed within a sphere of radius R. The electric field E … at a distance r from the centre for a point inside the atom is

”

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As charge is uniformly distributed over a sphere of radius R, the volume charge density inside the sphere is

.

Point charge of amount is located at the centre of the sphere. Therefore, the charge contained inside a sphere of radius r is

Therefore, electric field at a distance r from the centre of the sphere will be