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## Homework Statement

A uniformly charged solid sphere of radius R carries a total charge Q, and is set spinning with angular velocity [itex] \omega [/itex] about the z axis. (a) What is the magnetic dipole moment of the sphere?

## Homework Equations

[tex] \vec{m} = I \int d\vec{a} [/tex]

## The Attempt at a Solution

having a lot of difficulty with this stuff

since we are talking about a solid sphere ... first find volume current density [itex] J = \rho v[/itex]

[tex] \rho = \frac{Q}{\frac{4}{3} \pi R^3} [/tex]

[tex] v = \omega \times r = \omega r sin\theta [/tex]

so [tex] J = \frac{Q}{\frac{4}{3} \pi R^3} \omega r sin\theta [/tex]

is this ok so far??

alright now to find the total current [itex] I = \int J \cdot da [/itex]

[tex] I = \int \frac{Q}{\frac{4}{3} \pi R^3} \omega R^3 \sin^2\theta d\theta d\phi [/tex]

this doesnt seem dimensionally correct since the radians do not cancel out ...

where have i gone wrong??? Is it the part of the angular momentum??

thansk for your help