Capacitance of three coaxial metal tubes

[boardbox]

Homework Statement

Find the capacitance per unit length of three long coaxial metal tubes, with radii
a < b < c . A wire connects the innermost and outermost tubes (radii a and c).

Homework Equations

The Attempt at a Solution

I'm a little confused as to how I should set this up. What confused me is the wire that runs between the innermost and outermost tube. My thought is that it just makes the two tubes one big conductor. If that's the case and I put some charge on the conductor, how does it get distributed? Could I just put a charge on it and say the charge on the innermost tube is the area of the innertube over the area of the whole conductor times the charge?

 

[gabbagabbahey]

Could I just put a charge on it and say the charge on the innermost tube is the area of the innertube over the area of the whole conductor times the charge?

I don't think you can assume that. However, if the two cylinders are connected by a conducting wire, you can say that they are equipotentials.

 

[boardbox]

Alright well let me think this out for a second.

What I'm after is the potential from c to a, after that the problem is simple. That's going to be V(c) - V(a). Well V changes, so taking two steps V(c) - V(b) + V(b) - V(a). If V(c) = V(a) then I get zero potential. That seems a little silly to me, also means I'm dividing by zero in the next step, so I don't think that's right.

Here's another thought and this strikes me as a bit less silly. Say I have some charge on the innermost cylinder and some other charge on the middle cylinder. I could find the potential difference between the two. Now I know the outermost cylinder has the same potential at the innermost one, which means that the potential difference between it and the middle cylinder is the same as the difference between the middle cylinder and inner cylinder. So the potential of the set is just two times the potential between the inner and middle cylinder.

 

[gabbagabbahey]

What I'm after is the potential from c to a, after that the problem is simple.

Why do you say that? What is the applicable definition of capacitance here?