Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 71

A suggested scheme for reducing eddy-current power loss in transformer cores with a circular cross section is to divide the cores into a large number of small insulated filamentary parts. As illustrated in Fig., the section shown in part (a) is replaced by that in part (b). Assuming that B (t) = B 0 sin wt and that N filamentary areas fill 95% of the original cross-sectional area, find
a) the average eddy-current power loss in the section of core of height h in Fig.,
b) the total average eddy-current power loss in the N filamentary sections in Fig.
The magnetic field due to eddy currents is assumed to be negligible. ( Hin t: First find the current and power dissipated in the differential circular ring section of height h and width d r at radius r.)
FIGURE 1: Suggested eddy-current power-loss reduction scheme (Problem P.7-6).
(a)

FIGURE 2: Suggested eddy-current power-loss reduction scheme (Problem P.7-6).
(b)