# Capacitance of infinite cylinders

## Homework Statement

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

## 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?

## Answers and Replies

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

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
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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
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Gold Member

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.