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 3.4, Problem 3.32P
Two point charges, 3qand
Expert Solution & Answer
Learn your wayIncludes step-by-step video
schedule03:44
Students have asked these similar questions
Compute for the work done, in millijoules, in moving a 6-nC charge radially away from the center from a distance of 6 m to a distance of 12 m against the electric field inside a non-conducting spherical shell of inner radius 4 m, outer radius 18 m, and total charge 7 mC.answer: -3.1893 mJConsider two concentric conducting spherical shells of negligible thickness separated by vacuum. One of the shells has a radius of 4 m, while the other has radius of 8 m. The total charge of one of the shells is 7 mC, while that of the other is 8 mC. Their respective total charges are distributed evenly on their surfaces. Determine the total potential energy, in nanojoules, stored between the two shells. Use the permittivity of free space as 8.854 × 10-12 F/m.ans: -27.5250 ANSWER BOTH
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).
(b) Do the sphere and particle 1 have like charges or opposite charges?
Like charges
Opposite charges
Justify your claim.
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
22. A student has 65-cm-long arms. What is the minimum angular velocity (in rpm) for swinging a bucket of water...
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
If acceleration is proportional to the net force or is equal to net force.
Conceptual Physics (12th Edition)
When a gas expands along path AC shown below, it does 400 J of work and absorbs either 200 or 400 J of heat. (a...
University Physics Volume 2
120. Why can you drink a cup of boiling-hot tea atop a high mountain without any danger of burning your lips? W...
Conceptual Physical Science (6th Edition)
Must the potential be zero at any point where the electric field is zero? Explain.
Essential University Physics (3rd Edition)
Q25.16 (See Discussion Question Q25.14.) Will a light bulb glow more brightly when it is connected to a battery...
University Physics (14th Edition)
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
- An 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 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_forwardI have parts A & B. I just need help with c. The figure is attached. For the cylinder of uniform charge density in Fig. 2.26: (a) show that the expression there given for the field inside the cylinder follows from Gauss’s law My Answer: p = rho r<a: E = (p*r)/ (2 * epsilon not) r>a: E = (p * a^2)/(2 * epsilon * r) (b) find the potential φ as a function of r, both inside and outside the cylinder, taking φ = 0 at r = 0. My Answer: r<a: φ(r) = (-p * r^2)/(4 * epsilon not) r>a: φ(r) = (-p * a^2)/(4 * epsilon not) - (p * a^2)/(2 * epsilon not)(In(r/a)) c) Take the Laplacian in cylindrical coordinates and show that Poisson’s equation holds in this example.arrow_forward
- Two concentric spheres of radii R and R, are charged with surface charge densities o1 and 2, as shown in Fig. 3.arrow_forwardConsider a uniformly charged solid sphere of radius ? and total charge ? centered on the origin. In this problem you will calculate the potential ?(?) for ? < ? in two different ways. Use infinity as the reference point (i.e., ?(∞) = 0). (a) Use Eq. 2.21 of Griffiths to compute the potential at ? < ?. (b) Use Eq. 2.29 of Griffiths to compute the potential at ? < ?.arrow_forwardA cylindrically symmetric charge distribution has charge density p(r) given by P()= 2na erla where Op and a are constants. Calculate the total charge O contained within a cylinder of length I = 5a and radius 2a, centred on the z-axis, and grve your answer by entering numbers in both of the boxes in the equation below: [Note that you must enter a value in each of the boxes, including 1 or 0 if appropriate. Blank boxes will be marked as incorrect.]arrow_forward
- In spherical coordinates, V = -25 volts on a conductor at r = 2 cm and V = 150 volts at re 35 cm. The space between the conductors is a dielectric for which E,= 3.12. Find the surface charge densities on the conductors.arrow_forwardConsider a situation where a point charge q is located at the height of h above con- ducting ground. (The ground is in the potential V = 0.) (a) Calculate the force acting on the charge, assuming that the charge has a magnitude of q = +1 mC (which is 0.001 As), and the height is h = 1 m. What is the direction of the force? (Hint: the image principle might be helpful...) (b) Let's add another grounded conducting plane above the charge according to the figure, parallel to the original one, and the height d away from it. (In other words, now both planes are in the ground potential V = 0.) 2 Using again the image principle, find an equivalent charge constellation to replace the two conducting planes, such that the correct conductor boundary conditions are satisfied. (c) Compute the force acting on the charge in the case for d = 4h. Which direction is it? Is it larger or smaller than in the case of a single conductor?arrow_forwardA 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. b WODY 1. Find the electric field for rarrow_forwardFind the ratio of q/Q for the E-field to be zero at adistance of z = 3.59R for the charge distributionand geometry of problem #30 of the text. a isthe charge on the LARGER ring. Q is the chargeon the SMALLER ring. Answer in 5 Significant Figures!!arrow_forwardProbleisn t otherwise uniform electric field En. Find the resulting field within the cylinder. (The radius is a, the susceptibility xe, and the axis is perpendicular to Eo.) A very long cylinder of linear dielectric material is placed in anarrow_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_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
Ising model | A Bird's Eye View | Solid State Physics; Author: Pretty Much Physics;https://www.youtube.com/watch?v=1CCZkHPrhzk;License: Standard YouTube License, CC-BY