Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 3.4, Problem 3.45P
To determine
The electric potential inside and outside the cylinder.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem 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.]
Problem 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).
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 in three ways: a) direct integration, b) by superposition, and c) using the relationship for a force on a small patch.
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...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- 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.arrow_forwardProblem 3.18 The potential at the surface of a sphere (radius R) is given by Vo = k cos 30, where k is a constant. Find the potential inside and outside the sphere, as well as the surface charge density o (0) on the sphere. (Assume there's no charge inside or outside the sphere.)arrow_forwardProblem 2.28 Use Eq. 2.29 to calculate the potential inside a uniformly charged solid sphere of radius R and total charge q. Compare your answer to Prob. 2.21.arrow_forward
- 4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. (0, 5, 0) P-I nC/m 20° z-0 plane (0, 3, 0) p-3 Pu=1.5 nC/m 10° p-1.6 10° p-3.5 PacI nCim? 20 FIGURE 4.1Iarrow_forwardProblem 2.60 A point charge q is at the center of an uncharged spherical conducting shell, of inner radius a and outer radius b. Question: How much work would it take to move the charge out to infinity (through a tiny hole drilled in the shell)? [Answer: (q²/80) (1/a-1/b).]arrow_forwardFor problem 4 part b in square centimeters using inner and outer radii of the spherical capacitor of a = 2.00 cm and b = 1.05 a, respectively. (Answer in 5 sig. figs.)arrow_forward
- 4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. %3D (0, 5, 0)| PLA=A nC/m 20° z=0 plane (0, 3, 0) p= 3 PLB= 1.5 nC/m 10° 10° p=1.6 p= 3.5 Psc 1 nC/m2 20° FIGURE 4.11 See Prob. 20.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 << 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_forward4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. (0, 5, 0) PLA=A nC/m 20° z=0 plane (0, 3, 0) p=3 PLB=1.5 nC/m 10° 10° p= 1.6 p=3.5 Psc=1 nC/m² 20° FIGURE 4.11 See Prob. 20.arrow_forward
- W = 'fD-Edr. (4.58)arrow_forwardProblem 3.01. (a) Find the electric field between two plates which are separated along the y-axis Ay = 6.00 mm, where the bottom plate has a potential V₂ = 150. mV and the top plate has a potential V₁ = 5.00 mV. (b) What is the potential at a distance Ay' = 2.00 um from the bottom plate?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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
28.1 Rigid Bodies; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=u_LAfG5uIpY;License: Standard YouTube License, CC-BY