Exercises and Solutions on magnetism

1. Nickel is a ferromagnetic metal with density 8.90 g/cm3 . Given that Avogadro’s number NA = 6.02 × 10**23 atoms/mol and the atomic weight of Ni is 58.7, calculate the number of atoms of Ni per cubic metre. If one atom of Ni has a magnetic moment of 0.6 Bohr magnetons, deduce the saturation magnetization Ms and the saturation magnetic induction Bs for Ni.

2. The magnetization within a bar of some metal alloy is 1.2 × 106 A/m when the H field is 200 A/m. Calculate (a) the magnetic susceptibility χm of this alloy, (b) the permeability µ, and (c) the magnetic induction B within the alloy. What type(s) of magnetism would you suggest as being displayed by this material (and explain why)?

  3. Deduce the number of Bohr magnetons per atom of iron, given that the saturation magnetization Ms = 1.70 × 10**6 A/m, that iron has a BCC crystal structure, and that that the edge length of the cubic unit cell is 0.287 nm. Under certain conditions (e.g., in ultrathin films), iron can be grown with a FCC crystal structure. If Ms has approximately the same value as before and the number of Bohr magnetons per atom is the same as before, what does this allow you to say (if anything) about the edge length of the new cubic unit cell?

4. An iron bar magnet having a coercivity of 4000 A/m is to be demagnetized. If the bar is inserted within a cylindrical wire coil (a solenoid) 25 cm long and having 150 turns, what electric current is required to generate the necessary magnetic field?

 5. At any temperature T less than the critical temperature TC for a superconducting material, the critical field HC(T) depends approximately on temperature according to HC(T) = HC(0) [1 – (T/TC) 2 ] where HC(0) is the critical field at 0 K. Use this to do the following calculations. (a) Given that TC = 4.15 K and HC(0) = 3.27 × 104 A/m for mercury, calculate the critical magnetic fields for superconductivity to exist in mercury at temperatures of 2.0 K, 3.0 K, and 5.0 K. (b) To what temperature must mercury, initially at 10 K, be cooled in a magnetic field of 15,000 A/m for it to become superconducting?

6. Consider the following superconducting elements: Lead TC = 7.19 K HC(0) = 6.39 × 104 A/m Mercury TC = 4.15 K HC(0) = 3.27 × 104 A/m Tin TC = 3.72 K HC(0) = 2.41 × 104 A/m Assuming the same formula as in Question 5, deduce which of the above elements are superconducting at 2 K when placed in a magnetic field of 40,000 A/m.


Answers at the following link:

http://www.physics.uwo.ca/~mgc/MatSci-Assignment%203%20with%20answers.pdf