Page 292 - Engineering Electromagnetics, 8th Edition

274 ENGINEERING ELECTROMAGNETICS

Figure 8.16 See Problem 8.28.

8.29 In Problem 8.28, the linear approximation suggested in the statement of the
problem leads to flux density of 0.666 T in the central leg. Using this value
of B and the magnetization curve for silicon steel, what current is required in
the 1200-turn coil?
8.30 A rectangular core has fixed permeability µ r >> 1, a square cross section of
dimensions a × a, and has centerline dimensions around its perimeter of b
and d. Coils 1 and 2, having turn numbers N 1 and N 2 , are wound on the core.
Consider a selected core cross-sectional plane as lying within the xy plane,
such that the surface is defined by 0 < x < a,0 < y < a.(a)With current I 1
in coil 1, use Ampere’s circuital law to find the magnetic flux density as a
function of position over the core cross-section. (b) Integrate your result of
part (a)to determine the total magnetic flux within the core. (c) Find the
self-inductance of coil 1. (d) Find the mutual inductance between coils 1
and 2.
8.31 A toroid is constructed of a magnetic material having a cross-sectional area
of 2.5 cm and an effective length of 8 cm. There is also a short air gap of
2
2
0.25 mm length and an effective area of 2.8 cm .Anmmf of 200 A · tis
applied to the magnetic circuit. Calculate the total flux in the toroid if the
magnetic material: (a)is assumed to have infinite permeability; (b)is
assumed to be linear with µ r = 1000; (c)is silicon steel.

8.32 (a) Find an expression for the magnetic energy stored per unit length in a
coaxial transmission line consisting of conducting sleeves of negligible
thickness, having radii a and b.A medium of relative permeability µ r fills
the region between conductors. Assume current I flows in both conductors in
opposite directions. (b) Obtain the inductance, L, per unit length of line by
2
equating the energy to (1/2)LI .
8.33 A toroidal core has a square cross section, 2.5cm <ρ < 3.5 cm, −0.5cm <
z < 0.5 cm. The upper half of the toroid, 0 < z < 0.5 cm, is constructed of a
linear material for which µ r = 10, while the lower half, −0.5cm < z < 0,