The correct option is D 17ρr054ϵ0, towards left
Given,
Charge density or charge per unit volume=ρ
Radius of sphere =r0
If, Q is the total chrage on the sphere of radius r0, then
ρ=Q43πr30
Electric field on surface of the solid sphere at point B is given by
Ewhole sphere=Q4πϵ0r20=ρr03ϵ0...(1)
Electric field at a point outside the sphere at distance r is given by
Eo=Q4πϵ0r2=ρr303ϵ0r2
We can assume the spherical cavity to be made of material having charge density −ρ.
So, using above formula, the electric field at point B due to spherical cavity can be calculated by taking, rc=r02 and r=32r0,
Ecavity=ρ(r02)33ϵ0(3r02)2...(2)
So the net electric field at point B,
EB=Ewhole sphere−Ecavity
Substituting the values from equation (1) and (2),
EB=ρr03ϵ0(towards left)−ρ(r02)33ϵ0(3r02)2(towards right)
∴EB=17ρr054ϵ0, towards left.
Hence, option (a) is the correct answer.