Page 420 - Engineering Electromagnetics, 8th Edition

402 ENGINEERING ELECTROMAGNETICS

the antenna is an appreciable fraction of a wavelength, say λ/8. (a)An
antenna that is 12 cm long is operated in air at 1 MHz. What fraction of a
wavelength long is it? (b) The same antenna is embedded in a ferrite
material for which r = 20 and µ r = 2, 000. What fraction of a wavelength
is it now?
11.5 A 150 MHz uniform plane wave in free space is described by H s =
(4 + j10)(2a x + ja y )e − jβz A/m. (a) Find numerical values for ω, λ, and β.
(b) Find H(z, t)at t = 1.5 ns, z = 20 cm. (c) What is |E| max ?
11.6 A uniform plane wave has electric field
E s = (E y0 a y − E z0 a z ) e −αx e − jβx V/m. The intrinsic impedance of the
medium is given as η =|η| e , where φ is a constant phase. (a) Describe
jφ
the wave polarization and state the direction of propagation. (b) Find H s .(c)
2
Find E(x, t) and H(x, t). (d) Find < S > in W/m .(e) Find the
time-average power in watts that is intercepted by an antenna of rectangular
cross-section, having width w and height h, suspended parallel to the yz
plane, and at a distance d from the wave source.
11.7 The phasor magnetic field intensity for a 400 MHz uniform plane wave
propagating in a certain lossless material is (2a y − j5a z )e − j25x A/m.
Knowing that the maximum amplitude of E is 1500 V/m, find β, η, λ, ν p ,
r , µ r , and H(x, y, z, t).
11.8 An electric field in free space is given in spherical coordinates as
E s (r) = E 0 (r)e − jkr a θ V/m. (a) Find H s (r) assuming uniform plane wave
behavior. (b) Find < S >.(c) Express the average outward power in watts
through a closed spherical shell of radius r, centered at the origin. (d)
Establish the required functional form of E 0 (r) that will enable the power
flow in part c to be independent of radius. With this condition met, the given
field becomes that of an isotropic radiator in a lossless medium (radiating
equal power density in all directions).
11.9 A certain lossless material has µ r = 4 and r = 9. A 10-MHz uniform plane
wave is propagating in the a y direction with E x0 = 400 V/m and E y0 =
E z0 = 0at P(0.6, 0.6, 0.6) at t = 60 ns. Find (a) β, λ, ν p , and η;(b) E(y, t);
(c) H(y, t).
11.10 In a medium characterized by intrinsic impedance η =|η|e ,a linearly
jφ
polarized plane wave propagates, with magnetic field given as H s =
(H 0y a y + H 0z a z )e −αx − jβx . Find (a) E s ;(b) E(x, t); (c) H(x, t); (d) S .
e
11.11 A2 GHz uniform plane wave has an amplitude E y0 = 1.4 kV/m at (0, 0, 0,

t = 0) and is propagating in the a z direction in a medium where = 1.6 ×
10 −11 F/m, = 3.0 × 10 −11 F/m, and µ = 2.5 µH/m. Find (a) E y at

P(0, 0, 1.8 cm) at 0.2 ns; (b) H x at P at 0.2 ns.
11.12 Describe how the attenuation coefficient of a liquid medium, assumed to be
a good conductor, could be determined through measurement of wavelength