Is There a Potential Difference Across the Inner and Outer Walls of a Conductor?

[Juggernaut]

Homework Statement

Assume we have cavity in conductor. In the cavity we have +3q charge and conductor charge is distributed uniformly and is +7q.
With Gaus law we now that E=0 inside the conductor becaus Q enclosed is 0. But I have been wondering is there potential difference from inner wall to outer wall of conductor?
There is -3q in the inner wall and +4 outer wall and inside conductor E=0 so V= constant but is there potential leap between inner and outer wall?

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

Homework Statement

Assume we have cavity in conductor. In the cavity we have +3q charge and conductor charge is distributed uniformly and is +7q.
With Gaus law we now that E=0 inside the conductor becaus Q enclosed is 0. But I have been wondering is there potential difference from inner wall to outer wall of conductor?
There is -3q in the inner wall and +4 outer wall and inside conductor E=0 so V= constant but is there potential leap between inner and outer wall?

What makes you say that there is a potential difference?

 

[NascentOxygen]

I can't help with this, but I am trying to picture it. The charge distribution on the outside of a block of aluminium I can visualize. And I can picture a hole being drilled into the block. But how are you going to keep those 3q charges inside the hole? It's a conductor, so they will succeed in migrating to the outside and distributing themselves apart from the others.

These are static charges? Then I think there can be no potential difference between any two points on the conductor; the charges are free to move to reposition themselves so that all points on the surface of the conductor are at a uniform potential.

 

[Hootenanny]

I can't help with this, but I am trying to picture it. The charge distribution on the outside of a block of aluminium I can visualize. And I can picture a hole being drilled into the block. But how are you going to keep those 3q charges inside the hole? It's a conductor, so they will succeed in migrating to the outside and distributing themselves apart from the others.

It is not only the actual charge that is important, but the charge density on each surface. The outer surface is naturally larger and thus will require a greater total charge in order to have the same charge density as the inner surface, thus maintaining a zero field inside the conductor.

 

[Juggernaut]

well asume the conductor is spherical, and there's sphrical cavity in it. charge +3q in its origo, inner wall of conductor is 0-->a and outer wall is 0-->b.well if u draw Gaussian surface around the charge in the cavity then E is not zero, r<a, then there`d be potential difference inside the cavity, but if u draw GS a<r<b there's not. So I am thinking that just before the inner surface there's different potential than outside the conductor due to different charge of the surface...I know I explained it very hard way...Can I post here a picture?

E: Yes I can!

 

[Juggernaut]

here`s the picture! as you can see I am next Da Vince :D