Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 1.6, Problem 1.53P
(a)
To determine
The vector which can be represented as gradient of a scalar and the scalar function for that vector.
(b)
To determine
The vector which can be represented as curl of a vector function and the vector function for that vector.
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Students 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?
Problem 1.45. As an illustration of why it matters which variables you hold fixec
when taking partial derivatives, consider the following mathematical example. Le
w = ry and z = yz.
(a) Write w purely in terms of x and z, and then purely in terms of y and z.
(b) Compute the partial derivatives
and
and show that they are not equal. (Hint: To compute (ðu/dz)y, use i
formula for w in terms of r and y, not z. Similarly, compute (ðu/ar}:
from a formula for w in terms of only z and z.)
1.38 You lay a rectangular board on the horizontal floor and then tilt the board about one edge until it slopes at
angle 0 with the horizontal. Choose your origin at one of the two corners that touch the floor, the x axis pointing
along the bottom edge of the board, the y axis pointing up the slope, and the z axis normal to the board. You
now kick a frictionless puck that is resting at O so that it slides across the board with initial velocity (vox, voy, 0).
Write down Newton's second law using the given coordinates and then find how long the puck takes to return to
the floor level and how far it is from O when it does so.
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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