Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 3.3, Problem 3.25P
Find the potential outside an infinitely long metal pipe, of radius R, placed at right angles to an otherwise uniform electric field
Expert Solution & Answer
Trending nowThis is a popular solution!
Learn your wayIncludes step-by-step video
schedule02:12
Students have asked these similar questions
Problems
4.1 Dipole Moment Practice Find the electric dipole moment of:
(a) a ring with charge per unit length i = A, cos o where o is the angular variable in cylindrical coordinates.
Problem 4.22 A very long cylinder of linear dielectric material is placed in an
otherwise uniform electric field Eo. Find the resulting field within the cylinder. (The
radius is a, the susceptibility Xe, and the axis is perpendicular to Eo.)
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
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...
Additional Science Textbook Solutions
Find more solutions based on key concepts
An electromagnetic wave, such as light, does not require a medium. Can you think of an example that would suppo...
University Physics Volume 1
25. What is always increasing?
Conceptual Physical Science (6th Edition)
One way to measure blood flow when blood vessels are exposed during surgery is to use an electromagnetic flowme...
Essential University Physics: Volume 2 (3rd Edition)
Which of the three orientations of the moon at sunset, shown above, is most proper?
Conceptual Integrated Science
At the right is a sketch showing one of the atoms in the diffuse, cool cloud of gas described in the previous q...
Lecture- Tutorials for Introductory Astronomy
The mass of the object.
Physics (5th Edition)
Knowledge Booster
Similar questions
- An infinitely large horizontal plane carries a uniform surface charge density n = -0.280 nC/m². What is the electric field ✓? A proton is traveling in this field with initial speed strength in the region above the plane [Select] V01.00 x 105 m/s at 0 = 30° angle with respect to the plane, as shown in the figure below. Use the coordinate system in ✓? If the zero potential is the figure and neglect the effect of gravity. How high can the proton go [Select] at the origin level, i.e., y = 0 level, what is the potential energy [Select] height y21.00 m [Select] y [Select] 0 of the proton when it is at a height of y₁ = 0.500 m ? What is the proton's kinetic energy at Vo V 0 and kinetic energy Xarrow_forwardProblem 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 y pla R RA -d +d -Vo FIGURE 3.16 X +Voarrow_forwardProblem 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 Sann van véér véër riik dik WA WANA { 1 3 } a q FIGURE 3.15 Xarrow_forward
- Find a potential V for the following force in spherical coordinates. 1 F = 2rsinée, +rcos Gê, + ê. r sineVerify that this force is conservative by explicitly showing that the curl is zero.arrow_forwardLAPLACE In spherical coordinates with azimuthal symmetry, the general solution for the potential is given by +∞ V(r,0) = Air¹ +P₁(cos) Σ A₁r¹ l=0 Consider a specific charge density (0) = k cos³0, where k is constant, that is glued over the surface of a spherical shell of radius R. a. Solve for the potential inside the sphere. [15] Hint: Express the surface charge density as a linear combination of the Legendre polynomials.arrow_forwardConsider two point charges of equal magnitude q but opposite sign, separated by a dis- tance d (this is called an electric dipole). 1. Calculate the electric field set up by these two charges, for points in the xz-plane (the field will look the same in any plane containing the z-axis, because of rota- tional symmetry). Work in Cartesian coordinates, with the z-axis passing through the two charges, and the origin halfway between them; thus let the z-coordinate of the positive charge be d/2 and the z-coordinate of the negative charge -d/2. Show that the field is (x,0, z – d/2) (x,0, z + d/2) E(x,0, 2) = 4T€, ((x² + (z – d/2)²)³/2 (x² + (z + d/2)²)³/2, 2. Calculate the far-field approximation for points on the x-axis, i.e. approximate the field at points with z = 0 and with x> d. 3. Do the same for points on the z-axis, i.e. for x = 0 and z » d. Take care that your approximation is not too crude (a 0 answer won't do). To this purpose, bring the two terms of the solution on common…arrow_forward
- 2.10 A large parallel plate capacitor is made up of two plane conducting sheets with separation D, one of which has a small hemispherical boss of radius a on its inner surface (D > a). The conductor with the boss is kept at zero potential, and the other conductor is at a potenti al such that far from the boss the electric field between the plates is Ep. (a) Calculate the surface-charge densities at an arbitrary point on the plane and on the boss, and sketch their behavior as a function of distance (or angle). (b) Show that the total charge on the boss has the magnitude 3mé, Ega?. (c) If, instead of the other conducting sheet at a different potential, a point charge q is placed directly above the hemispherical boss at a distance d from its center, show that the charge induced on the boss is d - a? q' = -q 1 dyd + a?arrow_forwardProblem 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_forwardProblem 3.19The 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_forward
- Subject: Ideal Conductors and Capacitors A ring of mass m and radius r has charge -Q uniformly distributed around it. The ring is located a distance h from an infinite grounded conducting plane. Let z be the vertical coordinate with z = 0 taken to be the center of the infinite conducting plane. Find the electric field above the conducting plane at points on the axis of the ring. Your answershould be a function of Q, r, and h.arrow_forwardProblem 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_forwardProblem 4.32 A point charge q is imbedded at the center of a sphere of linear dielectric material (with susceptibility Xe and radius R). Find the electric field, the polarization, and the bound charge densities, ph and op. What is the total bound charge on the surface? Where is the compensating negative bound charge located?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