Question

A cavity is taken out from a uniform conducting sphere.Inside the cavity a dipole is placed such that its orientation is along the line joining centre to it.Find the potential at point P
(P is outside the sphere at a distance of R from centre of sphere and d from dipole's centre making an angle theta with perpendicular line to dipole )

Answer 1

Wouldn't the charges rearrange themselves to nullify the electric field due to the dipole, and so the potential due to inside of the sphere should be zero?

Answer 2

I don't get why will there be even the charges induced on the inner surface of the cavity when we don't have the net charge on dipole.

Answer 3

It's not just about net charge though. Have you heard of electrostatic shielding?

Answer 4

Yeah! Heard of that. When we place something in a conductor then that is shielded well from the electric field influence becoz we have 0 electric field inside a conductor.

Answer 5

Yeah, and conversely, the outside charges are shielded by the influence of the electric field of the inside charges too.
If the charges don't rearrange themselves, then the dipole would exert a net electric field at the point P.

Answer 6

You mean to say that when i place a charge outside a conductor then a charge is induced on the outer surface of conductor and if i draw a Gaussian surface just at the location of that ourside charge i will get a net 0 electric field.
I think this is what you mean

Answer 7

Hmm, I'm just saying that the net electric field on an outside point will only be due to the outer surface because of shielding. For everything inside the sphere though, the electric field amounts to zero.

As you said, drawing a Gaussian surface passing through point P would mean that the net electric flux is zero as the net enclosed charge is zero. But can we say that electric field is zero? Nah, I don't think so, because the situation isn't symmetrical.

Answer 8

But I'm still willing to bet that the answer is zero.

Answer 9

Okay ,you agreed that net flux is 0 and not electric field.
Lemme ask you just one thing then, isn't the elctric field uniform for the gaussian surface assumed at that outside point?

Answer 10

It's only uniform if it's spherically symmetrical, which I don't think it is. :|

Answer 11

I am unable to judge on what basis are you saying that it is not spherically symmetric.

Answer 12

Hmm OK cool... Can you prove that the electric fields at all points of the sphere will be equal? If so, then we can consider it.