Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2.5, Problem 2.38P
A metal sphere of radius R, carrying charge q, is surrounded by athick concentric metal shell (inner radius a, outer radius b, as in Fig. 2.48). The shell carries no net charge.
(a) Find the surface charge density
(b) Find the potential at the center, using infinity as the reference point.
(c) Now the outer surface is touched to a grounding wire, which drains off chargeand lowers its potential to zero (same as at infinity). How do your answers to(a) and (b) change?
Expert Solution & Answer
Learn your wayIncludes step-by-step video
schedule08:07
Students have asked these similar questions
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 4.1I
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).
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)
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.
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
Additional Science Textbook Solutions
Find more solutions based on key concepts
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective (8th Edition)
72. Two coupled boxcars are rolling along at 2.5 m/s when they collide with and couple to a third, stationary b...
College Physics: A Strategic Approach (4th Edition)
A plank, fixed to a sled at rest in frame S, is of length L0 and makes an angle of 0 with the xaxis. Later, the...
Modern Physics
The force, when you push against a wall with your fingers, they bend.
Conceptual Physics (12th Edition)
4.(I) What is the mass of the diver in Fig. 9-49 if she exerts a torque of 1800m. N on the board, relative the ...
Physics: Principles with Applications
Compare the brightness of the bulbs in this circuit. 1. What can you conclude from your observation about the a...
Tutorials in Introductory Physics
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
- The space between the plates of a parallel-plate capacitor (Fig. 4.24) is filled with two slabs of linear dielectric material. Each slab has thickness a, so the total distance between the plates is 2a. Slab-1 has dielectric constant of 2 and slab-2 has a dielectric constant of 1.5. With the area of each of the top and bottom conducting plates is much greater than a?, we can assume the the surface charge densities +o and -o on the top and bottom plates is uniform. (a) Find the electric displacement D in each slab. (b) Find the electric field E in each slab. (c) Find the potential difference between the plates. (d) Find the locations and amounts of all bound charge. (e) Based on the values of bound charge, recalculate E and verify your answer from (b). (f) How do your results relate to the formula for the addition of two series capacitors?arrow_forwardProblem 1: A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points A and B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to be moved from A to B, determine the following: What is The potential at A:.arrow_forward1.20P) An infinite line charge with line charge density of 2 located near an infinite, grounded conducting plane as shown in figure. Find the potential everywhere. Draw electric field lines and show equipotential surfaces. Calculate E field at the conductor surface due to the surface charges of o. Clearly indicate that, is the electric field and potential at the boundary surfaces are continuous or not (Explain your reasoning). The question has a linear charge density at the position x = a, y = b. ラメarrow_forward
- Problem 1: A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points A and B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to be moved from A to B, determine the following: What is The rate of change of the potential with respect to length or displacement in the conductorarrow_forwardAn isolated solid spherical conductor of radius 5.00 cm is surrounded by dry air. It is given a charge and acquires potential V, with the potential at infinity assumed to be zero. (a) Calculate the maximum magnitude V can have. (b) Explain clearly and concisely why there is a maximum.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
- I have the charge is d a charge o, riting at orizion- sumcounding Cubic bo z made of a perfect Conductor whose sides have length a. The domain of interest is volume Contained by box. a). Find expression of potential associated with this charge (This may be expression as sum). b). Find expression for surface charge density, one of inner walls of box (Again You can express this as sum). found onarrow_forwardI have the charge is d a charge o, riting at origion- Sumounding Cubic boz made of a perfect Conductor whose sides have length a. The domain of interest is volume Contained by box. a). Find expression of potential associated with this charge (This may be expression as sum). b). Find expression for surface charge density, one of inner walls of box (Again You can express this as sum). found onarrow_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_forward
- Problem 1: A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points Aand B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to bemoved from A to B, determine the following:b.) The electric potential energy at Barrow_forwardAn annulus with an inner radius of a and an outer radius of b has charge density and lies in the xy-plane with its center at the origin, as shown in (Figure 1). Figure σ b K 1 a Z 0 X 1 of 1 y Part A Using the convention that the potential vanishes at infinity, determine the potential at all points on the z-axis. Express your answer in terms of the electric constant €0, o, a, b, and z. IVE ΑΣΦΑΝΟ V = Submit Part B Request Answer Determine the x-, y-, z-components of the electric field at all points on the z-axis by differentiating the potential. Enter your answers separated by commas. Express your answers in terms of the electric constant €0, o, a, b, x, y, and z. Ex, Ey, Ez = Submit V ΑΣΦ Request Answer ? Ć www ?arrow_forwardWhat is the energy required to bring a point charge ? from very far to a distance ? from the center of an insulating sphere of radius ? with charge ?, assuming uniform charge density and d > R? What if the sphere is replaced with a hollow spherical conductor of charge -Q and radius R, what would the energy required be then? Hint: you don’t have to re-derive the potential due to a charged sphere again.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction 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 Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College 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