Question

A dipole is placed in front of s solid uncharged sphere the net potrntial at the surfsce of the sphere

Answer 1

Actual calculation is quite simple, in the sense that there are very few formulas; most of the solution is based on the basic principles and logic:

V on sphere, and V inside the sphere is the same V, because the sphere is a conductor.

So, we can choose any point within the sphere to calculate V. The most convenient point is the center of the sphere: V = Vcenter.

For any point P in space (not only inside the sphere but anywhere), Vp= Vdipole + Vinduced at this point.

For the center, Vinduced = 0, because all induced charges ar at the same distance from the center and the total induced charge is 0.

Hence, V = Vdipole at the center, and it is kpcos(θ)/d2kpcos(θ)/d2, where k depends on the units used(k = 1 in CGS /ESU and 1/4πϵ01/4πϵ0 in SI), dd is the distance from the dipole to the center of the sphere and θθ is the angle between dipole and direction to th