What is the magnetic dipole moment of a rotating charged record?

[stunner5000pt]

Homework Statement

A phonograph record of radius R carrying a unifrom surface charge sigma is rotating at a cosntant angular velocity omega. Find its magnetic dipole moment

Homework Equations

m = int I \bullet da

The Attempt at a Solution

Need to find the current first

well the sruface charge density is
K = \sigma \omega R

K = \frac{dI}{dl_{perp}}

where dl perp is the infinitesimal widthruning parallel to the flow of current
so here dl perp refers to circumference
I = \int K \bullet 2 \pi r dr??

is this even close to being right??
I fear i may have made some geomterical error..

thanks for your help!

 

[stunner5000pt]

ahh i got the answer using the equation

\vec{m} = \frac{1}{2} \int_{S} \vec{r}' \times \vec{K}(\vec{r'}) da'

da = r dr d\theta

thanks anyway!