Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356984
Author: ULABY
Publisher: PEARSON
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Chapter 5, Problem 36P
To determine
The proof that the relationship between
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I need a detailed solution to a
problem.
The far-zone electric field intensity (array factor) of an end-fire two-element array
antenna, placed along the z-axis and radiating into free-space, is given by
E=cos (cos - 1)
Find the directivity using
(a) Kraus' approximate formula
(b) the DIRECTIVITY computer program at the end of this chapter
Repeat Problem 2.19 when
E = cos
-jkr
0505π
$[
(cos + 1)
(a). Elmax = Cost (case-1)] | max"
= 1 at 8-0°.
0.707 Emax = 0.707.(1) = cos [(cose,-1)]
(cose-1) =
± 0,= {Cos' (2)
= does not exist
(105(0)=
90° = rad.
Bir
Do≈ 4T
ar=2() =
=
Bar
4-1-273 = 1.049 dB
T₂
a. Elmax = cos((cose +1)),
0.707 = cos (Close,+1))
= 1
at 6 = π
Imax
(Cose+1)=== G₁ = cos(-2) does not exist.
Girar=2()=π.
4T
\cos (0) + 90° + rad
Do≈ = +=1.273=1.049dB
IT 2
I need an expert mathematical solution.
The E-field pattern of an antenna. independent of , varies as follows:
0° ≤ 0≤ 45°
E = 0
45°
{1
90°
90° < 0 ≤ 180°
(a) What is the directivity of this antenna?
(b) What is the radiation resistance of the antenna at 200 m from it if the field is equal
to 10 V/m (rms) for Ø
=
0° at that distance and the terminal current is 5 A (rms)?
I need an expert mathematical solution.
The normalized far-zone field pattern of an antenna is given by
E =
{®
(sin
cos)/
0
Find the directivity using
0 ≤ 0 ≤ π and 0≤ 0≤ π/2.
3m2sds2,
elsewhere
Chapter 5 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 5.1 - What are the major differences between the...Ch. 5.1 - Prob. 2CQCh. 5.1 - How is the direction of the magnetic moment of a...Ch. 5.1 - If one of two wires of equal length is formed into...Ch. 5.1 - An electron moving in the positive x direction...Ch. 5.1 - A proton moving with a speed of 2 106 m/s through...Ch. 5.1 - A charged particle with velocity u is moving in a...Ch. 5.1 - A horizontal wire with a mass per unit length of...Ch. 5.1 - A square coil of 100 turns and 0.5 m long sides is...Ch. 5.2 - Two infinitely long parallel wires carry currents...
Ch. 5.2 - Devise a right-hand rule for the direction of the...Ch. 5.2 - What is a magnetic dipole? Describe its magnetic...Ch. 5.2 - Prob. 6ECh. 5.2 - A wire carrying a current of 4 A is formed into a...Ch. 5.2 - Prob. 8ECh. 5.3 - What are the fundamental differences between...Ch. 5.3 - Prob. 9CQCh. 5.3 - Compare the utility of applying the BiotSavart law...Ch. 5.3 - Prob. 11CQCh. 5.3 - A current I flows in the inner conductor of a long...Ch. 5.3 - The metal niobium becomes a superconductor with...Ch. 5.5 - What are the three types of magnetic materials and...Ch. 5.5 - What causes magnetic hysteresis in ferromagnetic...Ch. 5.5 - Prob. 14CQCh. 5.5 - The magnetic vector M is the vector sum of the...Ch. 5.6 - With reference to Fig. 5-24, determine the single...Ch. 5.7 - Prob. 15CQCh. 5.7 - What is the difference between self-inductance and...Ch. 5.7 - Prob. 17CQCh. 5.7 - Use Eq. (5.89) to obtain an expression for B at a...Ch. 5 - An electron with a speed of 8 106 m/s is...Ch. 5 - When a particle with charge q and mass m is...Ch. 5 - The circuit shown in Fig. P5.3 uses two identical...Ch. 5 - The rectangular loop shown in Fig. P5.4 consists...Ch. 5 - In a cylindrical coordinate system, a 2 m long...Ch. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - The loop shown in Fig. P5.9 consists of radial...Ch. 5 - An infinitely long, thin conducting sheet defined...Ch. 5 - An infinitely long wire carrying a 25 A current in...Ch. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - A circular loop of radius a carrying current I1 is...Ch. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Three long, parallel wires are arranged as shown...Ch. 5 - A square loop placed as shown in Fig. P5.20 has 2...Ch. 5 - Prob. 21PCh. 5 - Prob. 22PCh. 5 - Repeat Problem 5.22 for a current density J=zJ0er.Ch. 5 - In a certain conducting region, the magnetic field...Ch. 5 - Prob. 25PCh. 5 - Prob. 26PCh. 5 - Prob. 27PCh. 5 - A uniform current density given by J=zj0 (A/m2)...Ch. 5 - A thin current element extending between z = L/2...Ch. 5 - In the model of the hydrogen atom proposed by Bohr...Ch. 5 - Iron contains 8.5 1028 atoms/m3. At saturation,...Ch. 5 - The xy plane separates two magnetic media with...Ch. 5 - Given that a current sheet with surface current...Ch. 5 - In Fig. P5.34, the plane defined by x y = 1...Ch. 5 - The plane boundary defined by z = 0 separates air...Ch. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - A solenoid with a length of 20 cm and a radius of...Ch. 5 - Prob. 39PCh. 5 - The rectangular loop shown in Fig. P5.40 is...Ch. 5 - Determine the mutual inductance between the...
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