Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 3.4, Problem 3.49P
To determine
The proof that shows
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem 4.12 Calculate the potential of a uniformly polarized sphere (Ex. 4.2) directly from
Eq. 4.9.
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).
A particle of mass m, charge e, momentuun p scatters in the clectrostatic
potential produced by a spherically symmetric distribution of charge. You
are given the quantity f r²pdx = A, p(r) d³r being the charge in a vol-
ume element d³x. Supposing that p vanishes rapidly as r + ∞ and that
S pdx = 0; working in the first Born approximation, compute the differ-
ential cross section for forward scattering. (That is de lo-o, where 0 is the
scattering angle.)
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
Similar questions
- A right circular cylinder has an electrostatic potential of (p,4) on both ends. The potential on the curved cylindrical surface is zero. Find the potential at all interior points. 14.2.6 Hint. Choose your coordinate system and adjust your z dependence to exploit the symmetry of your potential.arrow_forwardA potential Vo(0) = k sin² (0/2) (k is a constant) is present on the surface of a hollow sphere ofradius R.1. Find the potential Vout(r, 0) outside the sphere (i.c., for r > R).arrow_forwardFind the gradient field F = Vo for the potential function o below. P(x,y.z) = In (3x +y° +z²) Vøxy.z) = (O Vo(x.y.z z)3Darrow_forward
- Problem #1 (Problem 5.3 in book). Come up with a function for A (the Helmholtz free energy) and derive the differential form that reveals A as a potential: dA < -SdT – pdV [Eqn 5.20]arrow_forwardSolve the shown integral and show is equal to one. prove it. please do then explain to me. thanks.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
- 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.]arrow_forwardThe following charge density function: (Po (1-r/R) for ≤R 55. The р = 0 elsewhere describes a long cylindrical charge distribution. Determine the electric field due to this charge distribution, everywhere.arrow_forwardUsing the condition (3.027) of Lect. 16, prove that the mo- mentum operator p is Hermitian. HINT: Use the periodic boundary conditions for the functions g(r) and s(x).arrow_forward
- Using what you learned in the Gradient section above, rewrite the differential form of Gauss's law, V·E = £, in terms of the clectric potential, V. You will obtain a Poisson сquation.arrow_forwardHow would I be able to sketch the graph in problem 7.36?arrow_forward1. Consider the 2D motion of a particle of mass u in a central force field with potential V(r). a) Find the r, o polar-coordinate expression of the Lagrangian for this system and write down the corresponding Euler-Lagrange e.o.m.s. b) Note that the angular variable o is cyclic. What is the physical interpretation of the correspond- ing integral of motion? (For the definitions of the italicized terms see this link.) c) Solve for o in terms of this integral of motion and substitute the result into the Euler-Lagrange equation for r. Show that the result can be arranged to look like a purely 1D e.o.m. of the form dVef(r) (1) dr Identify in the process the explicit expression for Vef(r), which will depend among other things on the integral of motion. d) Take now k V (r) = with k > 0 to be an attractive electrostatic/gravitational-type potential. Sketch the profile of the corresponding effective potential function Vef(r). Find the equilibrium solution for the correspond- ing e.o.m. (1). What…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