bfusco
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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.
J_b=\nabla \times M=0
and
K_b=M \times \hat{n}=Msin\theta \hat{\phi}
Apparently, I can treat this problem as a sphere rotating spherical shell, is that because the surface current K_b is in the \hat{\phi} direction?
So, if i can treat it as a rotating sphere, K=\sigma v, where v=R\omega
And using the Biot Savart law, I get to the point
B=\frac{\mu_0}{4\pi}\int (\sigma R \omega)(\hat{\phi} \times \hat{r})/r^2 dArea
Where r is the vector pointing from the source of the field to the point in question. for spherical coordinates I use (s,\theta,\phi)
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 \hat{\theta} direction because that is the only direction left for a sphere. I also am not entirely sure what r^2 is equal to. is it r^2=R^2+s^2-2Rcos\theta?