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 3.27P
A sphere of radius R, centered at the origin, carries charge density
Expert Solution & Answer
Learn your wayIncludes step-by-step video
schedule05:30
Students have asked these similar questions
A disk of radius R has a nonuniform surface charge density sigma = Cr, where C is a constant and r is measured from the center of the disk. Find (by direct integration) the potential at P.
A ring with radius R and a uniformly distributed total charge Q lies in the xy plane, centered at the origin.
What is the potential V(z) due to the ring on the z axis as a function of z?
What is the magnitude of the electric field E on the z axis as a function of z, for z>0?
What is the electric potential created by an arc with an irregular linear charge density λ = λ*Cos(Q), distributed with a radius of r = R at point O?
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
of internal resistance. Because each row has the same emf and the rows are connected together on each side, the...
College Physics
State the direction of the induced current for each case shown be1o obseMng from the sick of the magnet
University Physics Volume 2
Choose the best answer to each of the following. Explain your reasoning. About how many galaxies are there in a...
The Cosmic Perspective Fundamentals (2nd Edition)
A second experiment is performed in which glider D is fixed in place. Glider C is launched toward glider D with...
Tutorials in Introductory Physics
50. (I) Find the center of mass of the three-mass system shown in Fig. 7-37 relative to the 1.00-kg mass.
Physics: Principles with Applications
26. The earth’s radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on t...
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th 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
- (a) Find x L limit of the potential of a finite uniformly charged rod and show that it coincides with that of a point charge formula, (b) Why would you expect this result?arrow_forwardA uniformly charged ring with total charge q = 3.00 C and radius R = 10.0 cm is placed with its center at the origin and oriented in the xy plane. What is the difference between the electric potential at the origin and the electric potential at the point (0, 0, 30.0 cm)?arrow_forwardA sphere of radius R centered at the origin carries charge density ρ(r, θ) = k*(R/r^ 2) (R − 2r) sin θ where k is a constant, and r, θ are the usual spherical coordinates. Use the multipole expansion to find the approximate potential for points on the z-axis far from the sphere (z >> R).arrow_forward
- The general solution for the potential (spherical coordinates with azimuthal symmetry) is: +∞ ΣAir² + P₁(Cos 0) B₁ pl+1 l=0 V(r, 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. Solve for the potential inside the sphere. Hint: Express the surface charge density as a linear combination of the Legendre polynomials.arrow_forwardShow that electric potential for a shell whose radius is R, has charge q uniformly distributed on its entire surface, is the same as electric potential for a conductor (Solid) has radius R and charge q.arrow_forwardA ring of charge of radius a lies in the z = 0 plane and centered on the z-axis. The charge density on the ring is given by p(') = Peo cosp' [C/m]. First, find the electric field at any point on the z-axis, Ē(z). Next, find the potential Þ(z) on the z-axis. Explain why the field in this problem cannot be found by taking the gradient of your answer for Þ(z). xarrow_forwardUsing the general expression V(r,0) E (A,r BỊ + 1) P(cose) for the potential at a distance r from the center of a sphere shell of radius R. The acceptable expressions for potentials inside and outside the shell are: V (r,0) : E, Ar' P,(cose) (rarrow_forwardFind the potential on the z axis (0,0,h) produced by an annular(s) ring of uniform surface charge density p, in free space. The ring occupies the region z= 0, p≤a, 0≤ ≤27 in cylindrical coordinates.arrow_forwardThe right triangle has base b and height a with uniformly distributed surface charge density σ. The potential at the vertex P is: (answers in the image)arrow_forwardConsider a thick insulating spherical shell of a uniform volume charge density with a total charge Q = 6 Mu-C, an inner radius a = 10 mm, and an outer radius b = 60 mm. Find the electric potential for r = 55 mm.arrow_forwardA sphere of radius a has potential (sin 2θ)( cos ϕ) on its surface. Find the potential at all points outside the sphere.arrow_forwardA finite linear charge distribution has a total charge Q and length l. The linear charge density is uniform. The finite line is placed along the x-axis with the midpoint at the origin. Find the electric potential at point P, which is a distance z from the origin. Assume that the potential at infinity is zero.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY