A 1 kg steel rod and a 1 kg copper rod, each of identical cylindrical dimensions, are placed successively at the centre of the same induction heating coil driven at 20 kHz. The peak magnetic flux density at the rod position is 0.15 T. Some useful data are:
• Resistivity: steel 9.5×10−8Ωm, copper 1.7×10−8Ωm
• Relative permeability: steel 200, copper 1
• Specific heat capacity: steel 450 J kg⁻¹ K⁻¹, copper 385 J kg⁻¹ K⁻¹
Assume that the rms emf induced around a characteristic circular path inside each rod is directly proportional to μrfBA, where μr is the relative permeability and A the cross-sectional area (identical for both rods). The constant of proportionality is the same for the two materials.
(i) List two physical factors, other than resistivity, that influence the rate at which a conductor heats by eddy currents.
(ii) Using the above assumption, calculate the ratio of the initial heating powers developed in the steel rod and the copper rod when both are exposed to the same field.
(iii) Starting from room temperature (25 °C), determine which rod will reach 100 °C first, and justify your answer with a quantitative estimate based on their specific heat capacities and the power ratio obtained in part (ii).