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 3.38P
Here’s an alternative derivation of Eq. 3.10 (the surface charge density induced on a grounded
Expert Solution & Answer
Learn your wayIncludes step-by-step video
schedule07:30
Students have asked these similar questions
Figure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using superposition.
A cylindrically symmetric charge detribution has charge density p() gven by
-rla,
whare Oo and a ara constants. Calculate the total charge Q contained within a cylinder
of length L-Sa and radius 2a, centred on the z-axin, and give your answer by entering
numbers in both of the boxes in the equation below:
Figure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using direct integration.
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
Write each number in decimal form.
33. 1.4 × 100
Applied Physics (11th Edition)
If acceleration is proportional to the net force or is equal to net force.
Conceptual Physics (12th Edition)
The pV-diagram of the Carnot cycle.
Sears And Zemansky's University Physics With Modern Physics
(II) If 5.0L of antifreeze solution (specific gravity = 0.80) is added to 4.0 L of water to make a 9.0-L mixtur...
Physics for Scientists and Engineers with Modern Physics
Suppose you have a gas containing hydrogen molecules and oxygen molecules, in thermal equilibrium. Which molecu...
An Introduction to Thermal Physics
Set up the circuit with a single bulb and the battery combination as shown. Connect each probe of the voltmeter...
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
- Problem An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is 38 312 where Bis a constant and ris the distance from the center of the sphere. What is electric field at any point inside the sphere? Solution To find the electric field inside the non-uniformly charged sphere, we may apply integration method or the Gauss's Law method. Here, let us use the Gauss's law which is expressed as We will choose a symmetric Gaussian surface, which is the surface of a sphere, then evaluate the dot product to obcain (Equation 1) The issue however is how much charge does the Gaussian surface encoses? Since, our sphere is an insulating material. charges will get distributed non-uniformly within the volume of the object. So, we look into the definition of volume charge density to find the enclosed charge. So, we have dq p= dv Based on the given problem, we can also say that dgenc p= 38 dVarrow_forwardConsider linto. two The sphenical conductor (radius a) separetea latikude of ks from two parts at morth. The Parts. are insulated another One part (latitude s45') is top Potential of V and -V In. held at a bottom part Clattitude sphenical cocrdinates, take zaxis termss the at the of angle es painting where to north. In the two parts? Determine the entre are the electric potential space outside the Conductor.arrow_forward(ITV) (a) Solve the complete field solutions for the TE11 mode. At what location(s) on the x– y plane does the electric field have the maximum strength? (b) For the TE10 mode, calculate both the phase velocity v, and the group velocity vg, as well as their product v,*Vg. In HW V.2, we calculated the velocity of the energy propagation. Compare it to your answers and what can you conclude? Consider a square waveguide with all sides of equal length a.arrow_forward
- An Electron moves in the presence of a uniform magnesic field in The Z -direchin (B=Bk). Part a: write do wn a Vector potinh al A that generates the Specific magnhic field B. Assume A is independent of time and Az=0 Part b: Write down the darteoi ham iltonian for the system in terms of TTi , Where Tl; = P; -eAilc' is and e the electron Charge· * Part C:Compute [ TTe;T ly]arrow_forwardProblem An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is 3B p = 3/2 where B is a constant and r is the distance from the center of the sphere. What is electric field at any point inside the sphere? Solution To find the electric field inside the non-uniformly charged sphere, we may apply integration method or the Gauss's Law method. Here, let us use the Gauss's law which is expressed as PĒ - dÃ= We will choose a symmetric Gaussian surface, which is the surface of a sphere, then evaluate the dot product to obtain A = (Equation 1) The issue however is how much charge does the Gaussian surface encloses? Since, our sphere is an insulating material, charges will get distributed non-uniformly within the volume of the object. So, we look into the definition of volume charge density to find the enclosed charge. So, we have dq dV Based on the given problem, we can also say that dq enc p= 3B 13/2 dV Let us first…arrow_forwardFigure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << ahas been removed. What is the direction and magnitude of the fieldat the midpoint of the aperture? Solve this exercise using the relationship for a force on a small patch.arrow_forward
- Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0q)/( 242) Since, the actual ring (whose charge is dq) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ )(x0 2. ) We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E =…arrow_forwardC harge below. The. A neutral Conductor with a Cavity has a placed in its cavity as shown As shon electric flux the gavosian through Sur face enclosing the Conductor (as, shoon n fighre) EE=&E-JA =1 (10) N is found to be (a) Find the electric charge of t. (b) Fnd the Cmount of Charge on the inner Surface of the conductor. () Find the amount of Charge on the outkr Surface of the Conductor. Graussian Surfacearrow_forward2.6.1 Divergence Find hv.Edz, where E is the electric field due to a point charge q at x' and V is a sphere centered on the origin with radius b> |x'). please solve thisarrow_forward
- Figure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise in three ways: a) direct integration, b) by superposition, and c) using the relationship for a force on a small patch.arrow_forwardAn electric force is expressed as F = -pz sin o a, + p cos pa,. Transform F into cartesian coordinates and compute its magnitude at point (2,-1).arrow_forwardQuestion 2 a. Electrostatic fields have many applications, but most are low “low-power" applications; that is relatively low forces are involved. Explain why this is so. b. Given that D= (10ră ) ar (c/m²) in cylindrical coordinates, evaluate both sides of the divergence theorem for the volume enclosed by r= Im, r= 2m and Z= 0 and Z= 10arrow_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
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