Finding current of a revolving charged cylinder

[hangainlover]

Homework Statement

When given Q, ω, and geometry of a cylinder (radius a, length L)
how do you come up with current I*n ? the cylinder is rotating around the axis through the center of the cylinder

this question is essentially the same as finding magnetic field for a solenoid...
I just need to find what is equivalent to I*n in the B equation below...

IT's originally purcell 6.18...but i understand the question except how you come up with I*n (current times the number of turns for solenoid)

Homework Equations

B=(4pi/c)*(I*n)

The Attempt at a Solution

I thought Qω/(2pi) gives you the current..
I found the charge density Q/(2pi*a*L) multiplied it by L (because we want to find the flux of charge through a trip running parallel to the cylinder).
Then, multiplied it by the velocity (ω*a) which gives me Qω(2pi)..
However the answer says it has to be Qω/L ...

here is the solution i found...
http://www.6911norfolk.com/d0lbln/h7bs99/h7bs99-psoln9.pdf

 

[ideasrule]

I thought Qω/(2pi) gives you the current..

It does.

However the answer says it has to be Qω/L ...

It says the answer has to be Qv/L, where v is frequency. Since ω=2pi*f, this is identical to your formula.

 

[hangainlover]

But even then, my answer has an extra factor of L...