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## Homework Statement

Find the magnetic field of a uniformly magnetized sphere. (this is all that was given in the problem)

## The Attempt at a Solution

I chose the z axis in the same direction as M.

[tex]J_b=\nabla \times M=0[/tex]

and

[tex]K_b=M \times \hat{n}=Msin\theta \hat{\phi}[/tex]

Apparently, I can treat this problem as a sphere rotating spherical shell, is that because the surface current [itex]K_b[/itex] is in the [itex]\hat{\phi}[/itex] direction?

So, if i can treat it as a rotating sphere, [itex]K=\sigma v[/itex], where [itex]v=R\omega[/itex]

And using the Biot Savart law, I get to the point

[tex]B=\frac{\mu_0}{4\pi}\int (\sigma R \omega)(\hat{\phi} \times \hat{r})/r^2 dArea[/tex]

Where r is the vector pointing from the source of the field to the point in question. for spherical coordinates I use (s,[itex]\theta[/itex],[itex]\phi[/itex])

Im not entirely sure how to determine the direction of the cross product, because idk the direction of r, although i want to guess it is in the [itex]\hat{\theta}[/itex] direction because that is the only direction left for a sphere. I also am not entirely sure what [itex]r^2[/itex] is equal to. is it [itex]r^2=R^2+s^2-2Rcos\theta[/itex]?