Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Chapter 6, Problem 6.25P
A capacitor is formed from concentric spherical conductors having radii a and b, where b > a. The inner conductor is raised to potential V0; the outer conductor is grounded. Under these conditions, derive Eq. (39) using Laplace’s equation.
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Students have asked these similar questions
Derive the capacitance formula for the coaxial capacitor starting with Laplace’s equation. The voltage at the inner conductor is Vo and the outer conductor is 0 V. The formula obtained will match equation 6.28 in the book.
(a) Two parallel plates of area A separated by distance d form a capacitor. The first plate is
grounded and the second one has a potential V2.
Solving Laplace's equation determine:
(i)
(ii)
(iii)
(iv)
The potential between the plates
The electric field between the plates
The total charge on conductor 2
The capacitance.
The parallel plate capacitor in the figure below has a plate area A and plate
separation d. The capacitor is charged to a voltage Vo, and then isolated. A student
then inserts a dielectric slab (dielectric constant K) with thickness t and area A
between the plates and parallel to them as shown below (the dielectric does not
touch the plates at any time). Once the slab is in place, the student measures the
potential difference between the plates. What potential difference will the student
measure? You can assume the following numerical values: A=115.0 cm2, d=1.240 cm,
Vo=65.00 V, t=0.7800 cm and K=2.610.
O24.90 V
39.78 V
65.00 V
None of these
The answer will depend on the distance of the dielectric from the positive plate, which
is not provided in the problem
V
Chapter 6 Solutions
Engineering Electromagnetics
Ch. 6 - Prob. 6.1PCh. 6 - Let S = 100 mm2. d= 3 mm, and er = 12 for a...Ch. 6 - Capacitors tend to be more expensive as their...Ch. 6 - Prob. 6.4PCh. 6 - Prob. 6.5PCh. 6 - A parallel-plane capacitor is made using two...Ch. 6 - For the capacitor of Problem 6.6, consider the...Ch. 6 - Prob. 6.8PCh. 6 - Prob. 6.9PCh. 6 - A coaxial cable has conductor dimensions of a =...
Ch. 6 - Prob. 6.11PCh. 6 - (a) Determine the capacitance of an isolated...Ch. 6 - With reference to Figure 6.5, let b=6m, h=15m, and...Ch. 6 - Two=16 copper conductor (1.29 mm diameter) are...Ch. 6 - Prob. 6.15PCh. 6 - Prob. 6.16PCh. 6 - Construct a curvilinear-square map for a coaxial...Ch. 6 - Prob. 6.18PCh. 6 - Construct a curvilinear- square map of the...Ch. 6 - Prob. 6.20PCh. 6 - The inner conductor of the transmission line shown...Ch. 6 - Prob. 6.22PCh. 6 - Prob. 6.23PCh. 6 - A potential field in free space is given in...Ch. 6 - A capacitor is formed from concentric spherical...Ch. 6 - Given the spherical symmetric field in free space,...Ch. 6 - Let V=z(x,y)=4e2xf(x)3y2 in a region of free space...Ch. 6 - Show that in a homogeneous medium of conductivity...Ch. 6 - What total charge must be located within a unit...Ch. 6 - Prob. 6.30PCh. 6 - For the parallel-plate capacitor shown in Figure...Ch. 6 - Prob. 6.32PCh. 6 - The functions V1 (p, , z) and V2(p, , z) both...Ch. 6 - Prob. 6.34PCh. 6 - Prob. 6.35PCh. 6 - Prob. 6.36PCh. 6 - Prob. 6.37PCh. 6 - Prob. 6.38PCh. 6 - Prob. 6.39PCh. 6 - Prob. 6.40PCh. 6 - Prob. 6.41PCh. 6 - Prob. 6.42PCh. 6 - Prob. 6.43PCh. 6 - Prob. 6.44PCh. 6 - Prob. 6.45PCh. 6 - By appropriate solution of Laplaces and Poissons...
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