What Is the Capacitance of Coaxial Infinite Cylinders?

[Void123]

Homework Statement

I have two coaxial infinite cylinders and I must find their capacitance, where $$r_{1} < r_{2}$$

Homework Equations

The Attempt at a Solution

I got an answer (for finite cylinders) that is inversely proportional to $$Ln (r_{1}/r_{2})$$.

Assuming this answer is correct (if someone can check it), in order to make it infinite the two radii have to become infinitesimally small (0) correct? If I do this though, I get an indeterminate in the argument of log.

Have I done this wrong or must I rewrite my expression in terms of some approximate expansion?

 

[vela]

Are you sure the problem isn't asking you for the capacitance per unit length?

 

[Void123]

I am sure. I don't see how significant that is either, since I would just divide my expression by $$l$$. But, the road block at the moment is trying to infinitesimally minimize the radii so as to give me a finite solution.

 

[vela]

It's significant because the reason you get an infinite answer is because $l$ is infinite. Typically, this type of question asks you for the capacitance per unit length, which is a finite number.

 

[gabbagabbahey]

in order to make it infinite the two radii have to become infinitesimally small (0) correct?

No, in order two make the two cylinders infinitely long, you just make them longer.