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Magnetic dipole moment help

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1. 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


2. Homework Equations
[tex] m = int I \bullet da [/tex]


3. The Attempt at a Solution
Need to find the current first

well the sruface charge density is
[tex] K = \sigma \omega R [/tex]

[tex] K = \frac{dI}{dl_{perp}} [/tex]

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

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

thanks for your help!
 
Last edited:
1,444
2
ahh i got the answer using the equation

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

[tex] da = r dr d\theta [/tex]

thanks anyway!
 

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