Introduction to Electrodynamics
Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 1.6, Problem 1.57P
To determine

The value of integral and verify it using stokes theorem.

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1.1 Give a physical interpretation of what is meant by the curl of a vector. 1.2 Suppose a vector function A is given by A = -y i + x j and another vector function B is given by B = x j. Calculate (i) the curl of A: and (ii) the curl of B: 1.3 In which direction are the curls pointing? Hence what can you say about their divergence and why?
(a) Express the spherical unit vectors ê, ê, in terms of the Cartesian unit vectors ✰, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas, giving ✰, ŷ, 2 in terms of f, 0, $ (and 0, $). Calculate af/00 and af/ap, and express them in terms of spherical unit vectors. (b) Express the cylindrical unit vectors ŝ, , 2 in terms of the Cartesian unit vec- tors î, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverse formulas, giving x, ŷ, 2 in terms of ŝ, $, 2 (and ). Show that af/0 = $.
the surface S is defined by the sphere R? = x? + y + z?. Do the integral directly and also by using Gauss's theorem. 1-38. Find the value of the integral fs (V x A) da if the vector A = yi + zj + xk and Sis the surface defined by the paraboloid z = 1- x-y', where z2 0.

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Introduction to Electrodynamics

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