Worksheet for Magnetostatics in a material
1. An infinitely long copper wire of radius a is embedded in plastic insulation which increases the
overall radius to b. If the current density is uniform in the wire, find the magnetic field
everywhere. (Relative permeability of the copper is Km1 and that of the plastic is Km2.)
2. A coaxial cable can be modeled as two concentric cylinders, an inner one of radius R which
caries a total current I, and an outer one which is a tube of inner radius a and outer radius b, and
which carries a current I in the opposite direction. The space between is usually filled with a
plastic insulating material of relative permeability Km. Calculate the magnetic field
a) in the region R≤r≤a
b) outside the cable (r≥b)
3. (A research question) What is meant by the Curie temperature?
4. A cylindrical rod is made from a ferromagnetic material which has a permanent uniform
magnetization M = Mo k. (The axis of the rod is also the z axis.) Find the bound currents, and
show that the field that is produced is the same as that which would be obtained from a solenoid
with appropriate value for the current.
5. A sphere of radius R has a uniform magnetization M = Mo k. Calculate the magnetic moment of
the sphere
a) from the definition of the magnetization
b) from the bound currents
(note: you should get the same answer for each part.)
6. An infinitely large material has a uniform magnetization M. Embedded in the material is a
bubble of radius R. Show that the magnetic field at the centre is -⅔ μo M.