- #1

issacnewton

- 983

- 22

Here is a problem I am trying to do. A point charge q is located at a distance r

from the center O of an uncharged conducting spherical layer whose inside and

outside radii are equal to [itex]R_1[/itex] and [itex]R_2[/itex] respectively.

Find the potential at the point O if [itex]R_1 < R_2[/itex].

Now I was thinking of method of images. But since we have a spherical conducting

sphere with some thickness, that would mean we have several concentric equipotential

surfaces surrounding the chrge q. So one image charge would not suffice. We will

need infinitely many of the image charges. So method of images is not practical here. Griffiths

says in his book that the leftover charge on the outer surface in case of a charge

placed in a metal cavity is uniformly distributed. He doesn't give any satisfactory

reasoning. But let's assume what he says. Then the outside of the metal sphere, world

will see that charge q is at the center of the sphere, which means potential outside

is given by

[tex]V(r)=\frac{1}{4\pi\epsilon_o}\frac{q}{r}[/tex]

where r is the distance of any point outside the sphere from the center of

the sphere. So on the outer wall of the sphere, the potential is

[tex]V(R_2)=\frac{1}{4\pi\epsilon_o}\frac{q}{R_2}[/tex]

since sphere is metal , its equipotential, so the potential on the inner wall of the

sphere is same. So what else can we say so that we can get the potential at the

center of the sphere ?

thanks