Problem 3: Field of a Rotating Sphere (15 points)
A sphere of radius R carrying a uniform surface charge σ rotates with angular velocity ω about the z-axis.
σ
Z
ω
R
(b) Show that in the limit that the radius of the sphere goes to zero while the charge density increases to kept the magnetic moment constant, the magnetic field from Problem 3 is:
B(x) = $\frac{3\hat{r}(\hat{r} \cdot m)-m}{r^3} + \frac{8\pi}{3} m\delta(x)$
The last term is know as the "contact" field, and plays an important role in the hyperfine spectrum of atoms.
