Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Question
Chapter 1.6, Problem 1.57P
To determine
The value of integral and verify it using stokes theorem.
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Check out a sample textbook solutionStudents have asked these similar questions
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.
Chapter 1 Solutions
Introduction to Electrodynamics
Ch. 1.1 - Using the definitions in Eqs. 1.1 and 1.4, and...Ch. 1.1 - Prob. 1.2PCh. 1.1 - Prob. 1.3PCh. 1.1 - Prob. 1.4PCh. 1.1 - Prob. 1.5PCh. 1.1 - Prob. 1.6PCh. 1.1 - Prob. 1.7PCh. 1.1 - Prob. 1.8PCh. 1.1 - Prob. 1.9PCh. 1.1 - Prob. 1.10P
Ch. 1.2 - Prob. 1.11PCh. 1.2 - The height of a certain hill (in feet) is given by...Ch. 1.2 - Prob. 1.13PCh. 1.2 - Prob. 1.14PCh. 1.2 - Prob. 1.15PCh. 1.2 - Prob. 1.16PCh. 1.2 - Prob. 1.17PCh. 1.2 - Prob. 1.18PCh. 1.2 - Prob. 1.19PCh. 1.2 - Prob. 1.20PCh. 1.2 - Prob. 1.21PCh. 1.2 - Prob. 1.22PCh. 1.2 - Prob. 1.23PCh. 1.2 - Prob. 1.24PCh. 1.2 - Prob. 1.25PCh. 1.2 - Prob. 1.26PCh. 1.2 - Prob. 1.27PCh. 1.2 - Prob. 1.28PCh. 1.3 - Prob. 1.29PCh. 1.3 - Prob. 1.30PCh. 1.3 - Prob. 1.31PCh. 1.3 - Prob. 1.32PCh. 1.3 - Prob. 1.33PCh. 1.3 - Prob. 1.34PCh. 1.3 - Prob. 1.35PCh. 1.3 - Prob. 1.36PCh. 1.4 - Prob. 1.37PCh. 1.4 - Express the unit vectors in terms of (that is,...Ch. 1.4 - Prob. 1.39PCh. 1.4 - Prob. 1.40PCh. 1.4 - Prob. 1.41PCh. 1.4 - Prob. 1.42PCh. 1.4 - Prob. 1.43PCh. 1.5 - Evaluate the following integrals:
(a)
(b)
(c)...Ch. 1.5 - Prob. 1.45PCh. 1.5 - (a) Show that .
[Hint: Use integration by...Ch. 1.5 - Prob. 1.47PCh. 1.5 - Prob. 1.48PCh. 1.5 - Prob. 1.49PCh. 1.6 - (a) Let and . Calculate the divergence and curl...Ch. 1.6 - Prob. 1.51PCh. 1.6 - Prob. 1.52PCh. 1.6 - Prob. 1.53PCh. 1.6 - Prob. 1.54PCh. 1.6 - Prob. 1.55PCh. 1.6 - Prob. 1.56PCh. 1.6 - Prob. 1.57PCh. 1.6 - Prob. 1.58PCh. 1.6 - Prob. 1.59PCh. 1.6 - Prob. 1.60PCh. 1.6 - Prob. 1.61PCh. 1.6 - Prob. 1.62PCh. 1.6 - Prob. 1.63PCh. 1.6 - Prob. 1.64P
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