Capacitance of a System (Spherical Conducting Shells)

[GermanMC]

Homework Statement

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 ε_o. If the dielectric material is linear, what is the capacitance of the system?

Homework Equations

C=(Q/V)=4πε_o(ab/a-b)

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?

 

[GermanMC]

Homework Statement

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 ε_o. If the dielectric material is linear, what is the capacitance of the system?

Homework Equations

C=(Q/V)=4πε_o(ab/a-b)

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?

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

 

[rude man]

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

 

[GermanMC]

Bingo. Free charge didn't matter.

 

[rude man]

Bingo. Free charge didn't matter.

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.