# Capacitance of a cylinder containing an infinite number of cylinders

## Main Question or Discussion Point

I am a struggling physiology PhD student and would very much appreciate some help...

I need an expression for the capacitance of a cylinder (of finite radius and length) containing an infinite number of infinitely thin cylinders.

Any help would be greatly appreciated!

Many thanks,
-Ian

## Answers and Replies

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Meir Achuz
Science Advisor
Homework Helper
Gold Member
Your question is poorly posed. Capacitance is defined as the ratio of the charges on two conductors (+Q on one and -Q on the other) to the voltage (V) between them,
so C=Q/V. With an infinite number, what do you mean by capacitance?
Is the outer cylinder of finite length open or closed at the ends?

Chi Meson
Science Advisor
Homework Helper
Is the outside cylinder fully closed (that is, closed off at both ends)? If it is, then it does not matter what is inside it (I'm 90% sure of that, but someone correct me please).
Is there any separation between the outside cylinder and the inner ones? If not, then it would be identical to a solid cylinder, which would be identical (in capacitance) to a cylindrical shell.

Otherwise, the problem implies an infinitessimal distance between layers of a capacitor, which implies a capacitance that approaches infinity.