Finding potential at the center of metal sphere

[issacnewton]

ehild, in post # 58, I am talking about the inner spherical cavity which is not necessarily concentric with the outer spherical shell. You were replying to different question in post # 55. I just generalised that in post # 58.

 

[ehild]

I see. How do you get the potential at the outer surface then?

ehild

 

[issacnewton]

Ok

Irrespective of the shape of the cavity inside the metallic sphere, if we place the charge ,q,
inside the cavity, then equal charge q is distributed uniformly on the outer spherical surface.
The cavity and the outside are different worlds altogether as long as we are talking about
electrostatic case. So potential on the outer surface would just be $\frac{1}{4\pi\epsilon_o}\frac{q}{R_2}$

 

[rude man]

Ok

Irrespective of the shape of the cavity inside the metallic sphere, if we place the charge ,q,
inside the cavity, then equal charge q is distributed uniformly on the outer spherical surface.
The cavity and the outside are different worlds altogether as long as we are talking about
electrostatic case. So potential on the outer surface would just be $\frac{1}{4\pi\epsilon_o}\frac{q}{R_2}$

I agree with this of course, Issac. It's early in the morning for me but that sounds right.

As for your earlier query: as long as you can wrap a spherical Gaussian surface around the cavity and fully contained in metal, your statement must be true, otherwise the E field could not be zero everywhere about the surface. So it makes no difference what the shape of the metal is - it can be quite irregularly shaped - the charges in the cavity have to be distrtibuted so as to null the net field at every point on the Gaussian shell just beyond R1, just as in the concentric case. So the image would not change from the concentric c ase.