1) An infinitely long cylinder, of radius R, carries a
"frozen-in" magnetization (M), parallel to the axis
$\mathbf{M} = ks \hat{z}$.
where k is a constant and s is the distance from the axis;
there is no free current anywhere.
a. Find the volume current density $\mathbf{J}_b$.
b. Find the surface current density $\mathbf{K}_b$.
c. Calculate the auxiliary field H and B inside the
cylinder.
d. Calculate the auxiliary field H and B outside the
cylinder.
e. Sketch $\mathbf{J}_b$ and $\mathbf{K}_b$, Amperian's loop on the cylinder.
