Capacitance of three concentric shells

[Kashmir]

Homework Statement

A friend of mine sent me this problem about finding the capacitance.
We have three concentric shells of radius a, b, c. And we've to find the capacitance between x and y.

I need help.

Thank you

Relevant Equations

C=Q/V

I want to calculate the capacitance of this system between the points x&y.
So suppose I give a charge Q to the outermost shell and -Q to the innermost shell. To find the capacitance C, I try to find the potential V between the outermost shell and innermost shell .
To find V ,I integrate the electric field and find it out to be V=kq[1/a -1/c] where k=1/(4 *pi*epsilon). Then I can find C =Q/V.
Is this approach correct.

 

[kuruman]

This approach is correct. You should get the capacitance between the outer and inner shells the usual way as if the middle shell were not there. The middle shell is affecting nothing because it is an equipotential surface at the potential that would be there if there were vacuum between the shells.

A slightly more interesting problem might be to find the capacitance if a thick concentric shell were placed in between having wall thickness, say $d=\frac{1}{2}(c-a)$ with equal vacuum gaps between conductors.

 

[Kashmir]

This approach is correct. You should get the capacitance between the outer and inner shells the usual way as if the middle shell were not there. The middle shell is affecting nothing because it is an equipotential surface at the potential that would be there if there were vacuum between the shells.

A slightly more interesting problem might be to find the capacitance if a thick concentric shell were placed in between having wall thickness, say $d=\frac{1}{2}(c-a)$ with equal vacuum gaps between conductors.

Thank you. I’ll try your question :)

 

[haruspex]

You don't need to do any integration. Just write down the potential at radius a due to the two shells. You know that the potential due to the outer shell there is the same as it is at radius c.