# Electric potential in regions of concentric thin, conducing, spherical shells

1. Feb 3, 2004

### yanyin

two thin conducting spherical shells as shown below. the inner shell has a radius of r1=15.0cm and a charge of 10.0nC. the outer shell has a radius r2 = 30.0cm and a charge of -15.0nC. find the electric potential V in regions R1, R2, and outside the outer shell, with V = 0 at r = infinite.

2. Feb 3, 2004

### himanshu121

What is the expression for Potential due to a Spherical shell

In General

$$V=\frac{Q}{4\pi \epsilon_0 R} **&\mbox{for}** r \leq R$$

AND

$$V=\frac{Q}{4\pi \epsilon_0 r} **&\mbox{for}** r \geq R$$

Last edited: Feb 3, 2004
3. Feb 3, 2004

### rocketcity

I disagree with the above equations. From Gauss' law, a spherical shell does not contribute at all to the potential inside it--it's easier to think about with gravity: if the earth were hollow, you could float around in it; you wouldn't be attracted to any point on the shell.

So if you're inside the shell, you don't see it; if you're outside the shell then (again by an application of Gauss' law) it affects you in the same way that a concentric point charge of the same total charge would, i.e., a one over R potential.

That should get you started; you treat two shells with the superposition principle (i.e., add the two potentials together.)

P

4. Feb 3, 2004

### himanshu121

WHY it is not true

=> 0 which is not true.