Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356816
Author: Fawwaz T. Ulaby, Umberto Ravaioli
Publisher: PEARSON
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Textbook Question
Chapter 6, Problem 26P
The electric field radiated by a short dipole antenna is given in spherical coordinates by
Find H(R, θ; t).
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Students have asked these similar questions
50mV and 10kHz from the function generator to the input. The mulitmeter postive is connected to the output and negative to a ground. Is the circuit connected correctly? Yes or No. Does the reading look correct? I don't need calculations but will take them. I just need to know if the connection is right.
Connect a signal generator to the input and set it for 50 mV Sine wave with a frequency of 10 kHz. Connect the output to a multimeter set to RMS voltage. Record the output voltage and frequency in the following table. Repeat the measurement for all given frequency values in the table.
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
Chapter 6 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 6.2 - Explain Faradays law and the function of Lenzs...Ch. 6.2 - Prob. 2CQCh. 6.2 - Prob. 3CQCh. 6.2 - For the loop shown in Fig. 6-3, what is Vemftr if...Ch. 6.2 - Suppose that the loop of Example 6-1 is replaced...Ch. 6.4 - Suppose that no friction is involved in sliding...Ch. 6.4 - Is the current flowing in the rod of Fig. 6-10 a...Ch. 6.4 - For the moving loop of Fig. 6-9, find I when the...Ch. 6.4 - Suppose that we turn the loop of Fig. 6-9 so that...Ch. 6.5 - Contrast the operation of an ac motor with that of...
Ch. 6.5 - Prob. 7CQCh. 6.5 - Prob. 8CQCh. 6.7 - A poor conductor is characterized by a...Ch. 6.8 - When conduction current flows through a material,...Ch. 6.8 - Verify that the integral form of Ampres law given...Ch. 6.10 - Explain how the charge continuity equation leads...Ch. 6.10 - How long is the relaxation time constant for...Ch. 6.10 - Determine (a) the relaxation time constant and (b)...Ch. 6.11 - Prob. 7ECh. 6 - The switch in the bottom loop of Fig. P6.1 is...Ch. 6 - The loop in Fig. P6.2 is in the xy plane and B =...Ch. 6 - A coil consists of 100 turns of wire wrapped...Ch. 6 - A stationary conducting loop with an internal...Ch. 6 - A circular-loop TV antenna with 0.02 m2 area is in...Ch. 6 - The square loop shown in Fig. P6.6 is coplanar...Ch. 6 - The rectangular conducting loop shown in Fig. P6.7...Ch. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - A 50 cm long metal rod rotates about the z axis at...Ch. 6 - The loop shown in P6.11 moves away from a wire...Ch. 6 - The electromagnetic generator shown in Fig. 6-12...Ch. 6 - The circular, conducting, disk shown in Fig. P6.13...Ch. 6 - The plates of a parallel-plate capacitor have...Ch. 6 - A coaxial capacitor of length l = 6 cm uses an...Ch. 6 - The parallel-plate capacitor shown in Fig. P6.16...Ch. 6 - In wet soil, characterized by = 102 (S/m), r = 1,...Ch. 6 - An electromagnetic wave propagating in seawater...Ch. 6 - At t = 0, charge density v0 was introduced into...Ch. 6 - If the current density in a conducting medium is...Ch. 6 - Prob. 21PCh. 6 - If we were to characterize how good a material is...Ch. 6 - The electric field of an electromagnetic wave...Ch. 6 - The magnetic field in a dielectric material with ...Ch. 6 - Given an electric field E=xE0sinaycos(tkz), where...Ch. 6 - The electric field radiated by a short dipole...Ch. 6 - A Hertzian dipole is a short conducting wire...Ch. 6 - In free space, the magnetic field is given by...Ch. 6 - The magnetic field in a given dielectric medium is...
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