Page 293 - Engineering Electromagnetics, 8th Edition

CHAPTER 8 Magnetic Forces, Materials, and Inductance 275

Figure 8.17 See Problem 8.35.

has µ r = 20. An mmf of 150 A · t establishes a flux in the a φ direction.
For z > 0, find: (a) H φ (ρ); (b) B φ (ρ); (c) z>0 .(d) Repeat for z > 0.
(e) Find total .
8.34 Determine the energy stored per unit length in the internal magnetic field of
an infinitely long, straight wire of radius a, carrying uniform current I.

8.35 The cones θ = 21 and θ = 159 are conducting surfaces and carry total
◦
◦
currents of 40 A, as shown in Figure 8.17. The currents return on a spherical
conducting surface of 0.25 m radius. (a) Find H in the region 0 < r < 0.25,
21 <θ < 159 ,0 <φ < 2π.(b)How much energy is stored in this region?
◦
◦
8.36 The dimensions of the outer conductor of a coaxial cable are b and c, where
c > b. Assuming µ = µ 0 , find the magnetic energy stored per unit length
in the region b <ρ < c for a uniformly distributed total current I flowing
in opposite directions in the inner and outer conductors.
8.37 Find the inductance of the cone-sphere configuration described in
Problem 8.35 and Figure 8.17. The inductance is that offered at the origin
between the vertices of the cone.
8.38 A toroidal core has a rectangular cross section defined by the surfaces
ρ = 2 cm, ρ = 3 cm, z = 4 cm, and z = 4.5 cm. The core material has a
relative permeability of 80. If the core is wound with a coil containing 8000
turns of wire, find its inductance.
8.39 Conducting planes in air at z = 0 and z = d carry surface currents of
±K 0 a x A/m. (a) Find the energy stored in the magnetic field per unit length
(0 < x < 1) in a width w(0 < y < w). (b) Calculate the inductance per unit
1
2
length of this transmission line from W H = LI , where I is the total current
2
in a width w in either conductor. (c) Calculate the total flux passing through