An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negative charge up to a radius R. The atom as a whole is neutral. For this model, what is the electric field at a distance r from the nucleus ?

Explanation

The charge distribution for this model of the atom is as the total charge in the uniform sperical of charge z e + negative harge is neutral this immedialtely gives us the negative charge density p since we must have
`(4piR^(3))/(3) p= 0-Ze`
to fin d the electric field E(r ) at a point P which is a distance r away from the nucleus we use gauss law its direction is along the radius vector r from the origin to the point the obvious gaussian surface is a spherical surface centred to the point P the obvious gaussian surface is a spherical surface centred at the nucleus we consider two situation namely `rgtR` and `rlt R`
(i) `r gt R` the electric flux `Phi` enclosed by the spherical surface is `Phi =E(r )xx4 pi r^(2)`
where E(r ) is the magnitude of the electric field at r this is because the field at any point on the spherical and has the same magnitude at all points on the surface
i.e `q=Ze+(4pir^(3))/(3) P`
substituting for the charge density p obtained earlier we have M
(ii) `r gt R` in this case the total enclosed by the gaussian sperical surface is zero since the atom is neutral thus from gauss law
at r =R both cases given the same result E =0