Page 273 - Engineering Electromagnetics, 8th Edition

CHAPTER 8 Magnetic Forces, Materials, and Inductance 255

D8.8. Let the permittivity be 5 µH/m in region A where x < 0, and 20 µH/m
in region B where x > 0. If there is a surface current density K = 150a y −
200a z A/m at x = 0, and if H A = 300a x −400a y +500a z A/m, find: (a) |H tA |;
(b) |H NA |;(c) |H tB |;(d) |H NB |.

Ans. 640 A/m; 300 A/m; 695 A/m; 75 A/m

8.8 THE MAGNETIC CIRCUIT
In this section, we digress briefly to discuss the fundamental techniques involved in
solving a class of magnetic problems known as magnetic circuits. As we will see
shortly, the name arises from the great similarity to the dc-resistive-circuit analysis
with which it is assumed we are all familiar. The only important difference lies in the
nonlinear nature of the ferromagnetic portions of the magnetic circuit; the methods
which must be adopted are similar to those required in nonlinear electric circuits which
contain diodes, thermistors, incandescent filaments, and other nonlinear elements.
As a convenient starting point, let us identify those field equations on which
resistive circuit analysis is based. At the same time we will point out or derive the
analogous equations for the magnetic circuit. We begin with the electrostatic potential
and its relationship to electric field intensity,
E =−∇V (38a)
The scalar magnetic potential has already been defined, and its analogous relation to
the magnetic field intensity is

H =−∇V m (38b)

In dealing with magnetic circuits, it is convenient to call V m the magnetomotive force,
or mmf, and we shall acknowledge the analogy to the electromotive force, or emf,
by doing so. The units of the mmf are, of course, amperes, but it is customary to
recognize that coils with many turns are often employed by using the term “ampere-
turns.” Remember that no current may flow in any region in which V m is defined.
The electric potential difference between points A and B may be written as
B
E · dL (39a)
V AB =
A
and the corresponding relationship between the mmf and the magnetic field intensity,

B
V mAB = H · dL (39b)
A
wasdeveloped in Chapter 7, where we learned that the path selected must not cross
the chosen barrier surface.