Q1. Calculate the force between two flat circular coils each containing 10 turns of wire and carrying 5 A of current in the same direction of circulation, have mean radii of 0.2 m and are placed coaxially 0.01 m apart.

Q2. A piece of ferromagnetic material with constant relative permeability 5000 is placed in a uniform magnetic field. The material is in the shape of a spheroid and is placed with its longest axis parallel to the field. What is the ratio of the flux density B inside the body to the original flux density outside the body when the axial ratio of the spheroid is:

• 1:1 (a sphere),
• 5:1 (a prolate spheroid)
• 100:1 (also a prolatespheroid)

• Q 3. Describe howthe translational force on a magnetic material is related to the magnetic fieldand the properties of the material. The mass of a sample of paramagneticmaterial is being determined using a conventional force balance (i.e., bymeasuring its weight). However, in this case there is a magnetic field ofstrength 10⁶ A.m^-1 with a vertical field gradient of 2·10⁷A.m^-2 present. If the susceptibility of the material is 4·10^-4calculate the force on the sample and hence the error in the measured mass.
• Q 4. Iron has amagnetic moment of 2.22 Bohr magnetons per atom and a density of 7.87·10³ kg.m^-3.Calculate the expected magnetization of iron at 0 K and describe anyassumptions that you have made. How would you expect this magnetization of ironto vary as temperature is increased. How does the number of Bohr magnetons peratom change from 0 K to 300 K. Why does a piece of iron typically notexhibit high magnetization at room temperature (unless it has been“magnetized”)?