Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
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.
Expert Solution & Answer
Want to see the full answer?
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?
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Let vectors A =(2,1,−4), B =(−3,0,1), and C =(−1,−1,2).Calculate the following: What is the angle θAB between vector A and vector B?arrow_forwardThere are two numbers located on a plane represented mathematically by. A = (85 N, 180 N). And the other vector quantity is B = 140N with an angle of minus 10 degrees, Applying the method of the Law of Sines and Cosines, Determine: a) the magnitude and direction of the resultant force and b) the direction of the balancing force.arrow_forwardProve the property if a and b are vectors and m is a real number.(ma) . b = m(a . b)arrow_forward
- Let’s practice drawing some vectors. One the axes below, start at the origin and draw the givencomponent vectors and the resultant vector. Each line is one unit (a) |vx| = 2, |vy | = 3arrow_forwardLet’s practice drawing some vectors. One the axes below, start at the origin and draw the givencomponent vectors and the resultant vector. Each line is one unit (b) |vx| = −4, |vy | = 4arrow_forwardthe 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.arrow_forward
- Let vector A point from the origin into the second quadrant of the xy plane and vector B point from the origin into the fourth quadrant. The vector B −A must be in which quadrant?arrow_forward(a) Find the scalar products î · î, ĵ· ĵ, and k · Ê. (b) Find î · ĵ, ĵ · k, and k · î (c) Use the distributive law to multiply out the scalar product of two arbitrary vectors à Axî + Ayî + A¸k and B Equation 6.4. Bxî + Byĵ + Bzk, and use the results of (a) and (b) to verifyarrow_forwardFind the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provided round brackets.. (a) Oppositely directed to v = (7, -20) and half the length of v. W = (?, ?) (b) Length √13 and same direction as v = (1, 0, -5). (?, ?, ?) W =arrow_forward
- Consider the integral 2 dy S = + 12xy dx dr where y(x = 0) = 0 and y(x =1) =1. Find the function y(x) for which the integral S is an extremum.arrow_forwardLet vectors A=(2,1,−4), B=(−3,0,1), and C=(−1,−1,2).Calculate the following: What is the angle θAB between A and B?arrow_forwardAn alternative line definition Given a fxed point P,(xo- Yo) and a nonzero vector n = (a, b), the set of points P(x, y) for which PP is orthogonal to n is a line e (see figure). The vector n is called a normal vector or a vector normal to e. yA n = (a, b) P(x, y) Suppose a line is normal to n = (5, 3). What is the slope of the line?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY