Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Textbook Question
Chapter 3.2, Problem 3.11P
Two semi-infinite grounded
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Students have asked these similar questions
Problem 3.11 Two semi-infinite grounded conducting planes meet at right angles.
In the region between them, there is a point charge q, situated as shown in Fig. 3.15.
Set up the image configuration, and calculate the potential in this region. What
charges do you need, and where should they be located? What is the force on q?
How much work did it take to bring q in from infinity? Suppose the planes met
at some angle other than 90°; would you still be able to solve the problem by the
method of images? If not, for what particular angles does the method work?
y
b
V=0
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FIGURE 3.15
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Problem 3.11 Two semi-infinite grounded conducting planes meet at right angles.
In the region between them, there is a point charge q, situated as shown in Fig. 3.15.
Set up the image configuration, and calculate the potential in this region. What
charges do you need, and where should they be located? What is the force on q?
How much work did it take to bring q in from infinity? Suppose the planes met
at some angle other than 90°; would you still be able to solve the problem by the
method of images? If not, for what particular angles does the method work?
y
b
V=0
a
FIGURE 3.15
X
This one is tougher! A sphere of radius r has charge q.
(a) What is the infinitesimal increase in clectric potential energy dU if an infinitesimal
amount of charge dq is brought to infinity to the surface of the sphere?
(b) An uncharged sphere can acquire a total charge Q by the transfer of charge dq
over and over and over. Use your answer to part a to find an cxpression for the
potential energy of a uniformly-charged sphere of radius R with total charge Q.
Answer: U = 3_1 Q²
5 4tc0 R'
(c) Your answer to part b is the amount of energy nceded to assemble a charged
sphere. It is often called the self-energy of the sphere. What is the self-energy of
a proton, assuming it to be a charged sphere with a diamcter of 1.0 x 10 15 m?
Chapter 3 Solutions
Introduction to Electrodynamics
Ch. 3.1 - Find the average potential over a spherical...Ch. 3.1 - Prob. 3.2PCh. 3.1 - Prob. 3.3PCh. 3.1 - Prob. 3.4PCh. 3.1 - Prob. 3.5PCh. 3.1 - Prob. 3.6PCh. 3.2 - Find the force on the charge +q in Fig. 3.14....Ch. 3.2 - (a) Using the law of cosines, show that Eq. 3.17...Ch. 3.2 - In Ex. 3.2 we assumed that the conducting sphere...Ch. 3.2 - A uniform line charge is placed on an infinite...
Ch. 3.2 - Two semi-infinite grounded conducting planes meet...Ch. 3.2 - Prob. 3.12PCh. 3.3 - Find the potential in the infinite slot of Ex. 3.3...Ch. 3.3 - Prob. 3.14PCh. 3.3 - A rectangular pipe, running parallel to the z-axis...Ch. 3.3 - A cubical box (sides of length a) consists of five...Ch. 3.3 - Prob. 3.17PCh. 3.3 - Prob. 3.18PCh. 3.3 - Prob. 3.19PCh. 3.3 - Suppose the potential V0() at the surface of a...Ch. 3.3 - Prob. 3.21PCh. 3.3 - In Prob. 2.25, you found the potential on the axis...Ch. 3.3 - Prob. 3.23PCh. 3.3 - Prob. 3.24PCh. 3.3 - Find the potential outside an infinitely long...Ch. 3.3 - Prob. 3.26PCh. 3.4 - A sphere of radius R, centered at the origin,...Ch. 3.4 - Prob. 3.28PCh. 3.4 - Four particles (one of charge q, one of charge 3q,...Ch. 3.4 - In Ex. 3.9, we derived the exact potential for a...Ch. 3.4 - Prob. 3.31PCh. 3.4 - Two point charges, 3qand q , arc separated by a...Ch. 3.4 - Prob. 3.33PCh. 3.4 - Three point charges are located as shown in Fig....Ch. 3.4 - A solid sphere, radius R, is centered at the...Ch. 3.4 - Prob. 3.36PCh. 3.4 - Prob. 3.37PCh. 3.4 - Here’s an alternative derivation of Eq. 3.10 (the...Ch. 3.4 - Prob. 3.39PCh. 3.4 - Two long straight wires, carrying opposite uniform...Ch. 3.4 - Prob. 3.41PCh. 3.4 - You can use the superposition principle to combine...Ch. 3.4 - A conducting sphere of radius a, at potential V0 ,...Ch. 3.4 - Prob. 3.44PCh. 3.4 - Prob. 3.45PCh. 3.4 - A thin insulating rod, running from z=a to z=+a ,...Ch. 3.4 - Prob. 3.47PCh. 3.4 - Prob. 3.48PCh. 3.4 - Prob. 3.49PCh. 3.4 - Prob. 3.50PCh. 3.4 - Prob. 3.51PCh. 3.4 - Prob. 3.52PCh. 3.4 - Prob. 3.53PCh. 3.4 - Prob. 3.54PCh. 3.4 - Prob. 3.55PCh. 3.4 - Prob. 3.56PCh. 3.4 - Prob. 3.57PCh. 3.4 - Find the charge density () on the surface of a...
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