# Capacitance in concentric shells

## Homework Statement

Consider four concentric spherical metal
shells of radii r, 2r, 3r, and 4r. The middle
two shells are connected by wire, as shown.
What is the total capacitance of the system?

u= 1/2cv^2

## The Attempt at a Solution

So my teacher told us to assume we can hook it up to a battery(voltage) and that the two inner shells have the same charge and to evaluate the potential inner to outer, but I have no idea how to do this.

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vela
Staff Emeritus
Homework Helper
There's a number of details you'll have to figure out for yourself, but here's generally how to approach the problem. Assume there is a charge +Q on the inner sphere. Use Gauss's law to calculate the electric field between the spheres. You'll have to figure out what the charge of the other spheres as well. Once you know the electric field, you can integrate it to calculate the potential difference between the spheres.

So when I do that I get

E(r)= Q/4(pi)(R)2Epilsonknot

E(2r)=Q/4(pi)(2R)2Epilsonknot

E(3r)=Q/4(pi)(3R)2Epilsonknot

E(4r)=Q/4(pi)(4R)2Epilsonknot

Then I use V=Ed so I integrate this?

What am I integrating though, the difference between the electric fields or the distance?
I am stuck beyond this point and are my electric fields right?

vela
Staff Emeritus