Magnetic dipole moment help

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..

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