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 3.54P
To determine
The potential inside the pipe.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A 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).
2.1. Show that the volume element
3N
do =
Idq;dp;)
i=1
of the phase space remains invariant under a canonical transformation of the (generalized)
coordinates (q,p) to any other set of (generalized) coordinates (Q,P).
[Hint: Before considering the most general transformation of this kind, which
contact transformation, it may be helpful to consider a point transformation - one in which the
new coordinates Qi and the old coordinates q; transform only among themselves.]
referred to as a
2.10 A large parallel plate capacitor is made up of two plane conducting sheets with
separation D, one of which has a small hemispherical boss of radius a on its inner
surface (D > a). The conductor with the boss is kept at zero potential, and the
other conductor is at a potenti al such that far from the boss the electric field between
the plates is Ep.
(a) Calculate the surface-charge densities at an arbitrary point on the plane and
on the boss, and sketch their behavior as a function of distance (or angle).
(b) Show that the total charge on the boss has the magnitude 3mé, Ega?.
(c) If, instead of the other conducting sheet at a different potential, a point charge
q is placed directly above the hemispherical boss at a distance d from its center,
show that the charge induced on the boss is
d - a?
q' = -q 1
dyd + a?
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 particle moves in a potential given by U(x) = -7 x3 + 2.1 x (J). Calculate the location of the stable equilibrium of this potential, in m. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forwardA particle moves in a potential given by U(x) = -7 x5 + 52 x + 85 (J). Calculate the x coordinate of the stable equilibrium of this potential, in m. Note that your answer could be positive or negative. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forward2.1. Show that the volume element 3N do = Idq;dp;) i=1 of the phase space remains invariant under a canonical transformation of the (generalized) coordinates (q, p) to any other set of (generalized) coordinates (Q,P). [Hint: Before considering the most general transformation of this kind, which is referred to as a contact transformation, it may be helpful to consider a point transformation– one in which the new coordinates Q¡ and the old coordinates q; transform only among themselves.]arrow_forward
- Problem 3.36 (3rd edition): Two long straight wires, carrying opposite uniform line charges +1, are situated on either side of a long conducting cylinder (Fig. 3.39). The cylinder (which carries no net charge) has radius R, and the wires are a distance "a" from the axis. Find the potential at point 7. (Hint: you can use solution of problem 2.47) R a aarrow_forwardFor the scalar potential field f = x^2*y^3 + x*y^2*z^3 + c, what is the direction and magnitude of the steepest decent at point P(1,2,1) and calculate the directional derivative in the direction of u(2,1,2) at the point P?arrow_forwardA heavy rope, 60 ft long, weighs 0.3 Ib/ft and hangs over the edge of a building 130 ft high. (Let x be the distance in feet below the top of the building. Enter x,* as x;.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. 3 lim 10*i i = 1 Express the work as an integral. 60 dx 10* Evaluate the integral. 540 V ft-lb (b) How much work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim 0.3x Express the work as an integral. 30 0.3x dx Jo Evaluate the integral. 135 X ft-lbarrow_forward
- Is the force feld F placian of scalar potential for F. O- COS x + z°)l+ (2y sinx – 4)) (3X2" + 2)R a conservative flela? I Prove that the vector A = 3y*z²i+4x³z²j – 3x²y²k at (1,1,-6) is solenoidal.arrow_forwardwhat is the most general potential V(x(t)) for which equation of motion x(t) is linear (Please type answer no write by hend)arrow_forwardFigure 2.72 For Prob. 2.8. 2.5 For the network graph in Fig. 2.69, find the number of nodes, branches, and loops.arrow_forward
- Verify that each of the following force fields is conservative. Then find, for each, a scalar potential o such that F = -Vo. F = (3x²yz − 3y)i + (x³z − 3x)j + (x³y + 2z)k.arrow_forwardA particle of charge −q and mass m is placed at the center of a uniformly charged ring of total charge Q and radius R. The particle is displaced a small distance along the axis perpendicular to the plane of the ring and released. Assuming that the particle is constrained to move along the axis, show that the particle oscillates in simple harmonic motion with a frequency (in picture attached).arrow_forwardCan you do problem number 6.23 the easiest way for me to understand and a sketch please ?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