Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.2, Problem 2.17P
To determine
The relation between electric field and distance where electric field is a function of distance.
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Figure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using superposition.
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Fig.
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WODY
1. Find the electric field for r
Problem 2.01. Three plates with surface charge density |o| = 8.85 μC/mm² are stacked on top of each
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Chapter 2 Solutions
Introduction to Electrodynamics
Ch. 2.1 - (a) Twelve equal charges,q, arc situated at the...Ch. 2.1 - Find the electric field (magnitude and direction)...Ch. 2.1 - Find the electric field a distance z above one end...Ch. 2.1 - Prob. 2.4PCh. 2.1 - Prob. 2.5PCh. 2.1 - Find the electric field a distance z above the...Ch. 2.1 - Find the electric field a distance z from the...Ch. 2.2 - Use your result in Prob. 2.7 to find the field...Ch. 2.2 - Prob. 2.9PCh. 2.2 - Prob. 2.10P
Ch. 2.2 - Use Gauss’s law to find the electric field inside...Ch. 2.2 - Prob. 2.12PCh. 2.2 - Prob. 2.13PCh. 2.2 - Prob. 2.14PCh. 2.2 - A thick spherical shell carries charge density...Ch. 2.2 - A long coaxial cable (Fig. 2.26) carries a uniform...Ch. 2.2 - Prob. 2.17PCh. 2.2 - Prob. 2.18PCh. 2.2 - Prob. 2.19PCh. 2.3 - One of these is an impossible electrostatic field....Ch. 2.3 - Prob. 2.21PCh. 2.3 - Find the potential a distance s from an infinitely...Ch. 2.3 - Prob. 2.23PCh. 2.3 - Prob. 2.24PCh. 2.3 - Prob. 2.25PCh. 2.3 - Prob. 2.26PCh. 2.3 - Prob. 2.27PCh. 2.3 - Prob. 2.28PCh. 2.3 - Prob. 2.29PCh. 2.3 - Prob. 2.30PCh. 2.4 - Prob. 2.31PCh. 2.4 - Prob. 2.32PCh. 2.4 - Prob. 2.33PCh. 2.4 - Find the energy stored in a uniformly charged...Ch. 2.4 - Prob. 2.35PCh. 2.4 - Prob. 2.36PCh. 2.4 - Prob. 2.37PCh. 2.5 - A metal sphere of radius R, carrying charge q, is...Ch. 2.5 - Prob. 2.39PCh. 2.5 - Prob. 2.40PCh. 2.5 - Prob. 2.41PCh. 2.5 - Prob. 2.42PCh. 2.5 - Prob. 2.43PCh. 2.5 - Prob. 2.44PCh. 2.5 - Prob. 2.45PCh. 2.5 - If the electric field in some region is given (in...Ch. 2.5 - Prob. 2.47PCh. 2.5 - Prob. 2.48PCh. 2.5 - Prob. 2.49PCh. 2.5 - Prob. 2.50PCh. 2.5 - Prob. 2.51PCh. 2.5 - Prob. 2.52PCh. 2.5 - Prob. 2.53PCh. 2.5 - Prob. 2.54PCh. 2.5 - Prob. 2.55PCh. 2.5 - Prob. 2.56PCh. 2.5 - Prob. 2.57PCh. 2.5 - Prob. 2.58PCh. 2.5 - Prob. 2.59PCh. 2.5 - Prob. 2.60PCh. 2.5 - Prob. 2.61P
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- Figure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using direct integration.arrow_forward(b) A smaller metal sphere, also mounted on an insulating plastic stand, is uncharged. This smaller sphere is moved close to the positively charged sphere. Fig. 1.1 shows the two spheres. positively charged sphere I-I smaller sphere plastic stands Fig. 1.1 (i) On Fig. 1.1, draw the distribution of charge on the smaller sphere. (ii) An earthed metal wire is touched against the smaller metal sphere. Štate and explain what happens to the charge on the smaller sphere. (c) Explain, in terms of their structures, why the metal wire is an electrical conductor but the plastic stand is an electrical insulator.arrow_forwardProblem 2.20 One of these is an impossible electrostatic field. Which one? (a) E= k[xy x + 2yz y + 3xz 2]; (b) E= k[y² + (2xy + z²)ŷ + 2yz2]. Here k is a constant with the appropriate units. For the possible one, find the poten- tial, using the origin as your reference point. Check your answer by computing VV. [Hint: You must select a specific path to integrate along. It doesn't matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a definite path in mind.]arrow_forward
- A point charge +Q is placed at the centre of an uncharged spherical conducting shell of inner radius a and outer radius b as shown in Fig. 2.51. Fig. 53 b. ~ 1. Find the electric field for rarrow_forwardProblem 2.20 One of these is an impossible electrostatic field. Which one? (a) E =k[xyÂ+2yzý+3xz2]; (b) E = k[y² + (2xy + z²)ý + 2yz 2). Here k is a constant with the appropriate units. For the possible one, find the potential, using the origin as your reference point. Check your answer by computing VV. [Hint: You must select a specific path to integrate along. It doesn't matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a particular path in mind.]arrow_forwardProblem 2.20 One of these is an impossible electrostatic field. Which one? (a) Ek[xy x + 2yzý + 3xz2]; (b) E= k[y² + (2xy + z²) ŷ + 2yz 2]. Here k is a constant with the appropriate units. For the possible one, find the potential, using the origin as your reference point. Check your answer by computing VV. [Hint: You must select a specific path to integrate along. It doesn't matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a particular path in mind.] Problem 2.11 Use Gauss's law to find the electric field inside and outside a spherical shell of radius R, which carries a uniform surface charge density o. Compare your answer to Prob. 2.7. Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V (r).arrow_forwardAn insulating solid sphere of radius 3 m has 15 C of charge uniformly distributed throughout its volume. Calculate the charge contained in a Gaussian surface having a radius 1/2 that of the sphere. Present your answer accurately to 2 decimal numbers i.e 3.20. Do not include units!arrow_forwardProblem 3.35 A solid sphere, radius R, is centered at the origin. The "northern” hemisphere carries a uniform charge density po, and the "southern" hemisphere a uniform charge density -po. Find the approximate field E(r, 0) for points far from the sphere (r » R).arrow_forwardFigure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << ahas been removed. What is the direction and magnitude of the fieldat the midpoint of the aperture? Solve this exercise using the relationship for a force on a small patch.arrow_forwardProblem 2.9Suppose the electric field in some region is found to be E = kr³î, in spherical coordinates (k is some constant). (a) Find the charge density p. (b) Find the total charge contained in a sphere of radius R, centered at the origin. (Do it two different ways.)arrow_forward2.12 Use Gauss' law to determine the E field produced by a spherical charge distribution of density p = a/r2, where a is a constant.arrow_forward4.17 Let E xya, + x'a,, find %3D (a) Electric flux density D. (b) The volume charge density py.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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