Page 317 - Engineering Electromagnetics, 8th Edition

CHAPTER 9 Time-Varying Fields and Maxwell’s Equations 299

total conduction current I c through the capacitor; (c) the total displacement
current I d through the capacitor; (d) the ratio of the amplitude of I d to that
of I c , the quality factor of the capacitor.
9.12 Find the displacement current density associated with the magnetic field
H = A 1 sin(4x) cos(ωt − βz) a x + A 2 cos(4x) sin(ωt − βz) a z .
9.13 Consider the region defined by |x|, |y|, and |z| < 1. Let r = 5, µ r = 4, and
2
8
σ = 0. If J d = 20 cos(1.5 × 10 t − bx)a y µA/m (a) find D and E;(b) use
the point form of Faraday’s law and an integration with respect to time to
find B and H;(c) use ∇× H = J d + J to find J d .(d) What is the numerical
value of b?
9.14 Avoltage source V 0 sin ωt is connected between two concentric conducting
spheres, r = a and r = b, b > a, where the region between them is a
material for which = r 0 , µ = µ 0 , and σ = 0. Find the total
displacement current through the dielectric and compare it with the source
current as determined from the capacitance (Section 6.3) and
circuit-analysis methods.
9.15 Let µ = 3 × 10 −5 H/m, = 1.2 × 10 −10 F/m, and σ = 0everywhere.
10
If H = 2 cos(10 t − βx)a z A/m, use Maxwell’s equations to obtain
expressions for B, D, E, and β.
9.16 Derive the continuity equation from Maxwell’s equations.
9.17 The electric field intensity in the region 0 < x < 5, 0 < y <π/12, 0 < z <
10
0.06 m in free space is given by E = C sin 12y sin az cos 2 × 10 ta x V/m.
Beginning with the ∇× E relationship, use Maxwell’s equations
to find a numerical value for a,ifitis known that a is greater than zero.
9.18 The parallel-plate transmission line shown in Figure 9.7 has dimensions
b = 4cmand d = 8 mm, while the medium between the plates is
characterized by µ r = 1, r = 20, and σ = 0. Neglect fields outside the
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dielectric. Given the field H = 5 cos(10 t − βz)a y A/m, use Maxwell’s

Figure 9.7 See Problem 9.18.