Magnetic dipole moment

[stunner5000pt]

1. The problem statement, all variables and given/known data
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


2. Relevant equations
m = int I \bullet da


3. 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!