- #1

Eitan Levy

- 259

- 11

- Homework Statement
- An infinite cylinder shell with a radius equal to R is rotating with a radial velocity ω around an axis located in its center. The density of the charge on the shell is σ. Find the inductance of the cylinder per unit-length.

- Relevant Equations
- I=dq/dt

0.5LI^2=U

First, the correct answer is μ0*π*R^2.

I tried to look at the cylinder like it was a solenoid, this technique was used in my class.

Then I tried to find the current of the solenoid, to do that I looked at a piece of a solenoid with a legnth of dz, then:

I=dq/dt=(2πRσ*dz)/(2π/ω)=ω*R*σ*dz.

The density of the loops in that case would be n=1/dz. Therefore the magnetic field inside is B=μ0*ω*R*σ.

The problematic part was to find the inductance. Both ways I tried failed.

First, I tried to use L=(magnetic flux)/(current).

The magnetic flux, if we look at a piece with a length equals to L, would be μ0*ω*σ*π*R^3*(L/dz). But dividing this by the current gives a very off answer and I can't get rid of dz.

Another approach was to use U=0.5LI^2 but it suffers from the same problem.

Obviously I am doing something very wrong, but can't understand what exactly. Can anyone help please?

I tried to look at the cylinder like it was a solenoid, this technique was used in my class.

Then I tried to find the current of the solenoid, to do that I looked at a piece of a solenoid with a legnth of dz, then:

I=dq/dt=(2πRσ*dz)/(2π/ω)=ω*R*σ*dz.

The density of the loops in that case would be n=1/dz. Therefore the magnetic field inside is B=μ0*ω*R*σ.

The problematic part was to find the inductance. Both ways I tried failed.

First, I tried to use L=(magnetic flux)/(current).

The magnetic flux, if we look at a piece with a length equals to L, would be μ0*ω*σ*π*R^3*(L/dz). But dividing this by the current gives a very off answer and I can't get rid of dz.

Another approach was to use U=0.5LI^2 but it suffers from the same problem.

Obviously I am doing something very wrong, but can't understand what exactly. Can anyone help please?