Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356984
Author: ULABY
Publisher: PEARSON
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Textbook Question
Chapter 7, Problem 27P
At 2 GHz, the conductivity of meat is on the order of 1 (S/m). When a material is placed inside a microwave oven and the field is activated, the presence of the electromagnetic fields in the conducting material causes energy dissipation in the material in the form of heat.
- (a) Develop an expression for the time-average power per mm3 dissipated in a material of conductivity σ if the peak electric field in the material is E0.
- (b) Evaluate the result for an electric field E0 = 4 × 104 (V/m).
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Students have asked these similar questions
The input reactance of an infinitesimal linear dipole of length A/60 and radius a=A/200
is given by
Xin = – 120
[In(€/a) — 1]
tan(ke)
Assuming the wire of the dipole is copper with a conductivity of 5.7 x 10' S/m,
determine at f = 1 GHz the
(a) loss resistance
(b) radiation resistance
(c) radiation efficiency
(d) VSWR when the antenna is connected to a 50-ohm line
Example
Solve the octic polynomial
2x⁸-9x⁷+20x⁶-33x⁵+46x⁴-66x³+80x²-72x+32=0
Solution
Divide by x⁴
2x⁴-9x³+20x²-33x+46-66/x + 80/x² - 72/x³ + 32/x⁴=0
Combine and bring terms
2(x⁴+16/x⁴) - 9(x³+8/x³) +20(x²+4/x²)-33(x+2/x) + 46= 0
Let use substitution
Let x+2/x =u
(x+2/x)²= u²
x²+2x*2/x + 4/x² = u²
x²+4/x²= u²-4
(x+2/x)³= x³+8/x³+3x*2/x(x+2/x)
u³= x³+8/x²+6u
x³+8/x³= u³-6u
(x²+4/x²)²= x⁴+2x²*4/x² + 16/x⁴
(u²-4)²= x⁴+16/x⁴ + 8
x⁴+16/x⁴ = (u²-4)²-8
x⁴+16/x⁴ = u⁴-8u²+8
2(u⁴-8u²+8)-9(u³-6u)+20(u²-4)-33u+46=0
Expand and simplify
2u⁴-9u³+4u²+21u-18=0
After checking
(u-1)(u-2) Are factors
Then
2u²-3u-9=0
u=3, u=-3/2
Assignment question
Solve the octic polynomial
2s⁸+s⁷+2s⁶-31s⁴-16s³-32s²-160=0 using the above example question, please explain in detail
b)
Another waveform g(t) is defined by
=0
t≥0, α>0
otherwise
g(t)= At exp(-at)
and is plotted in Figure 1 (for representative values of 4 = 1 and α = 1).
g(t)
0.4T
0.3+
0.2
0.1+
2
0
2
Figure 1
8
c)
Show that its amplitude spectrum is |G(@)| = -
A
(a²+0²)²
Describe briefly, with the aid of labelled sketches, how changing a affects
the waveform in both the time and frequency domains.
d) Deduce the Fourier transform H(@) of h(t) = g(t)+g(t+b)+g(t-b) and
calculate its DC amplitude H(0).
Chapter 7 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 7.2 - What is a uniform plane wave? Describe its...Ch. 7.2 - Since E and H are governed by wave equations of...Ch. 7.2 - If a TEM wave is traveling in the y direction, can...Ch. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - If the magnetic field phasor of a plane wave...Ch. 7.2 - Repeat Exercise 7-3 for a magnetic field given by...Ch. 7.3 - An elliptically polarized wave is characterized by...Ch. 7.3 - Prob. 5CQCh. 7.3 - The electric field of a plane wave is given by...
Ch. 7.4 - If the electric field phasor of a TEM wave is...Ch. 7.4 - The constitutive parameters of copper are = 0 = 4...Ch. 7.4 - Prob. 8ECh. 7.4 - For a wave traveling in a medium with a skin depth...Ch. 7.5 - Prob. 6CQCh. 7.5 - In a good conductor, does the phase of H lead or...Ch. 7.5 - Prob. 8CQCh. 7.5 - Is a conducting medium dispersive or...Ch. 7.5 - Compare the flow of current through a wire in the...Ch. 7.6 - Convert the following values of the power ratio G...Ch. 7.6 - Find the voltage ratio g corresponding to the...Ch. 7 - The magnetic field of a wave propagating through a...Ch. 7 - Prob. 2PCh. 7 - The electric field phasor of a uniform plane wave...Ch. 7 - The electric field of a plane wave propagating in...Ch. 7 - A wave radiated by a source in air is incident...Ch. 7 - The electric field of a planewave propagating in a...Ch. 7 - The magnetic field of a plane wave propagating in...Ch. 7 - A 60 MHz plane wave traveling in the x direction...Ch. 7 - Prob. 9PCh. 7 - For a wave characterized by the electric field...Ch. 7 - Prob. 11PCh. 7 - The magnetic field of a uniform plane wave...Ch. 7 - A linearly polarized plane wave of the form...Ch. 7 - The electric field of an elliptically polarized...Ch. 7 - Compare the polarization states of each of the...Ch. 7 - Plot the locus of E(0, t) for a plane wave with...Ch. 7 - Prob. 17PCh. 7 - Prob. 18PCh. 7 - In a medium characterized by r = 9, r = 1, and =...Ch. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - The skin depth of a certain nonmagnetic conducting...Ch. 7 - Prob. 24PCh. 7 - The electric field of a plane wave propagating in...Ch. 7 - The magnetic field of a plane wave propagating in...Ch. 7 - At 2 GHz, the conductivity of meat is on the order...Ch. 7 - In a nonmagnetic, lossy, dielectric medium, a 300...Ch. 7 - A rectangular copper block is 30 cm in height...Ch. 7 - Prob. 30PCh. 7 - The inner and outer conductors of a coaxial cable...Ch. 7 - Prob. 32PCh. 7 - The magnetic field of a plane wave traveling in...Ch. 7 - A wave traveling in a nonmagnetic medium with r =...Ch. 7 - The electric-field phasor of a uniform plane wave...Ch. 7 - Prob. 36PCh. 7 - A wave traveling in a lossless, nonmagnetic medium...Ch. 7 - At microwave frequencies, the power density...Ch. 7 - Consider the imaginary rectangular box shown in...Ch. 7 - Repeat Problem 7.39 for a wave traveling in a...Ch. 7 - Given a wave with E=x E0 cos(t kz): (a) Calculate...Ch. 7 - Prob. 42P
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