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**1. Homework Statement**

Find the magnetic dipole moment of a spherical shell of radiu R carrying a uniform surface charge sigma, set spinning at angular velocity omega.

**2. Homework Equations**

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

**3. The Attempt at a Solution**

So we gotta figure out the surface charge density (since it is a spherical shell)

[tex] K = \sigma v [/tex]

and [tex] v = \omega times R [/tex]

this is where i am doubtful...

the angle between v and R varies from 0 to 2 pi

so this cross product is not unique...

or am i thinking about this the wrong way??

please help!