2. A ferromagnetic sphere of radius b is magnetized uniformly with a magnetization M = \hat{z}M_0. Determine the equivalent
magnetization current densities (volume and surface) inside the magnet and at its surface, and calculate the magnetic field
intensity and flux density at the center of the sphere.
Take-aways: This is very similar to the permanent electric polarization problem from a previous homework. Does anyone
remember Buckyballs?
3. A solenoidal coil is centered along the z-axis, carrying a current I and having n turns per unit length. The sense (direction)
of the current is such that the coil's magnetic dipole moment points in the +\hat{z} direction. The radius of the coil is b, and it
is long enough that it can be treated as being infinite in extent as far as the fields are concerned (as in the class example).
a) What are B and H everywhere, using the infinite solenoid approximation?
b) If a cylindrical rod of radius a < b, made out of a magnetic material with permeability \mu, is then inserted coaxially
into the solenoid, what are B, H, M, and the equivalent magnetic current densities?
Take-aways: Draw as many parallels to capacitance and materials/dielectrics as you can, as the patterns and procedures
for inductance and capacitance can be very helpful in solving problems.
