Question

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

Answer 1

Charge on nucleus is =+Ze

total negative charge =−Ze(∵ atoms is electrical neutral)

Negative charge density, ρ=volumecharge=34πR3−Ze

i.e., ρ=−43πR3Ze...(i)

Consider a Gaussian surface with radius r

By Gauss's theorem

ϕ=E(r)×4πr2=ε0q....(ii)

Charge enclosed by Gaussian surface

q′=Ze+34πr3ρ=Ze−ZeR3r3 [Using (i)]

From (ii)

E(r)=4πε0r2q′=4πε0r2Ze−ZeR3r3