Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose we have a cylindrical shell of radius $r$ with surface charge density $\sigma$. Then we start rotating the cylinder at an angular speed $\Omega$. You can show that in this case the surface current density on the cylinder is $\sigma r \Omega$.

Similarly, in a solenoid with loop density $n$ and current $I$, the surface current density can be thought to be $nI$, so you can use this to "convert" between a rotating cylinder and a solenoid. For example, the magnetic field inside the cylindrical shell must be $\mu_0 \sigma r \Omega$, because for the solenoid it's $\mu_0 n I$.

I was wondering if you could establish another relation between the solenoid and the cylinder if the solenoid has a resistance $R$. Based on the analogy, I imagine the resistance must be connected to the cylinder's moment of inertia, but I can't quite figure it out.

share|cite|improve this question

If you use ampere's law, you will find that the magnetic field inside the rotating cylinder is uniform. With some fiddling, you will get that the magnetic field is equivalent to a solenoid with an infinite number of loops per length with a $\sigma r \Omega \mathrm{d}l$ current in each loop (a differential amount of current in each loop).

share|cite|improve this answer
This answer does not address the OP's question about resistance. – ZachMcDargh Mar 22 '14 at 17:58

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.