# Capacitance of a System (Spherical Conducting Shells)

1. May 2, 2012

### GermanMC

1. The problem statement, all variables and given/known data
A spherical conducting shell of radius 0.1 m has a free charge of -2 μC. It is surrounded by a concentric spherical conducting shell of radius 0.12 m carrying a free charge of -2 μC. Between the shells is a dielectric material of dielectric constant 10 εo. If the dielectric material is linear, what is the capacitance of the system?

2. Relevant equations
C=(Q/V)=4πεo(ab/a-b)

3. The attempt at a solution

I attempted the solution with only the above equation, I'm just not sure how to to include the dielectric constant in my answer. The instructions say that I should use one of Maxwell's Equations. How do I make the connections I need?

2. May 2, 2012

### GermanMC

Nvm, I feel that I have the kinks worked out.

3. May 2, 2012

### rude man

I was gonna say, the first thing is to ignore the bit about the -2μC charges!

4. May 2, 2012

### GermanMC

Bingo. Free charge didn't matter.

5. May 2, 2012

### rude man

It might have if the dielectric were nonlinear, but colleges don't pull stuff like that on you!
(In that case, C would have to be defined as dq/dV instead of q/V, or "incremental capacitance" instead of just "capacitance". Many types of real-life capacitors do display some nonlinearity, matter of fact.