Question 19.12

When a metal is heated its density decreases. This is for two reasons: thermal expansion of the solid; and the formation of vacancies. Consider a specimen of copper at 20 C with a density of 8940 kg/m³.

1. Determine its density on heating to 1000 C if only thermal expansion is concerned.
2. Repeat the calculation including the formation of vacancies. Assume that the energy of vacancy formation is 0.9 eV/atom, and that the volume coefficient of thermal expansion, alpha_v, is three times the linear coefficient, alpha_l.

Question 19.26

Derive Equation 19.8

sigma = E * alpha_l * (T₀-T_f)

from Equation 19.3:

(l_f - l₀)/l₀ = alpha_l(T₀-T_f)

Question 19.D2

The ends of a cylindrical rod 6.4 mm in diameter and 250 mm long are mounted between rigid supports. The rod is stress-free at 20 C, and can withstand a tensile stress of up to 138 MPa. If the rod has to survive being cooled to - 60 C, which of the following materials could it be made from: aluminium, copper, brass, 1025 steel, or tungsten?

Question 20.2

A coil of wire 0.1m long and having 15 turns carries a current of 1.0A.

1. Compute the flux density if the coil is in a vacuum
2. A bar of an iron -silicon alloy, the B-H behaviour of which is shown in Figure 20.24, is placed in the coil. What is the flux density in the bar?
3. If the bar of iron-silicon is replaced by a bar of molybdenum, what current must be used to produce the same field in the molybdenum as was produced in the iron-silicon alloy by the 1.0-A current?

Question 20.7

The magnetization within a bar of some metal alloy is 1.2 * 10⁶ A/m at an H field of 200 A/m. Compute the magnetic susceptibility, permeability and magnetic flux density within the material. What types of magnetism are displayed by the material? What is the evidence for this?

Question 20.10

Consider a hypothetical metal having ferro-magnetic behaviour, a simple cubic crystal structure, an atomic radius of 0.125 nm, and a saturation flux density of 0.85 tesla. Find the number of Bohr magnetons per atom for this material.

Question 20.21

Schematically sketch on a single plot the B-H behaviour for a ferromagnetic material at 0 K, and at temperatures just below and just above its Curie temperature. Briefly explain why these curves have different shapes.

Question 20.28

An iron bar magnet having a coercivity of 4,000 A/m is to be demagnetised. If the bar is inserted in a cylindrical wire coil 0.15 m long and having 100 turns, what electric current is required to generate the necessary magnetic field?