Introduction to Electrodynamics
Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.3, Problem 2.24P
To determine

To Calculate:The potential difference between a point on the axis and a point on the outer cylinder.

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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).
Find a potential V for the following force in spherical coordinates. 1 F = 2rsinée, +rcos Gê, + ê. r sineVerify that this force is conservative by explicitly showing that the curl is zero.
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?

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Introduction to Electrodynamics

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