Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 1.2, Problem 1.22P
(a)
To determine
Divergence of two vectors.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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.)
1.1
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 hinged rigid bar of length l is connected by two springs of stiffnesses K1 and K2 and is subjected to a force F as shown in Fig. 1.33(a). Assuming that the angular displacement of the bar (θ) is small, find the equivalent spring constant of the system that relates the applied force F to the resulting displacement x.
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
Similar questions
- Problem 1.15 Calculate the divergence of the following vector functions: (a) va = x² + 3xz²ŷ - 2xz2.arrow_forwardProblem 2.16 The divergence of a vector F is given by 1 a(pF,) , 13F, , ƏF, V.F = + az Evaluate V · F for F(p.0.2) = pp+z sin ø4+Jpzk. Answer: 2+zcoso/p+VP/z.arrow_forward1.32 In the Eigen vector equation AX = X, the operator A is given 32 A = 41 Find: (a) The Eigen values (b) The Eigen vector X (c) The modal matrix C and it's inverse C-1 (d) The product C-1 ACarrow_forward
- Prove that for any vector u, u = (u e,)e, +(u ·e, )e, + (u e,)e,. [Hint: write u in component form.] Find the projection of the vector u e, -2e, +e, on the vector 2. 3. v = 4e, - 4e, + 7e,.arrow_forwardIn general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A = (1,0, -3), B=(-2,5,1), and =(3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas. ▸ Part A ▸ Part B Part C -A+B-C-(0,4,3) Submit 15. ΑΣΦ Part D * Incorrect; Try Again; 9 attempts remaining 3A-2C - Previous Answers Request Answer 195] ΑΣΦ ? BHO ?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_forward
- 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.arrow_forwardProblems 5.1 Determine the material derivative of the flux of any vector property Qj through the spatial area S. Specifically, show that in agreement with Eq 5.2-5. 1999 by CRC Press LLC 5.2 Let the property P in Eq 5.2-1 be the scalar 1 so that the integral in that equation represents the instantaneous volume V. Show that in this case dV = 5.3 Verify the identity !! and, by using this identity as well as the result of Problem 5.1, prove that the material derivative of the vorticity flux equals one half the flux of the curl of the acceleration; that is, show that 5.4 Making use of the divergence theorem of Gauss together with the identity aw at show that w,v, - dtarrow_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_forward
- Suppose an aircraft is flying with Euler angles equal to (Y,0,Ð) = (+225,+45,-45) deg. a) With g = 32.174 ft/s², compute g., gy, ge (in units of ft/s²). b) With (U,V,W) = (+500,-25,+50) ft/s, compute X, Ý, ¿ (in units of ft/s).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_forwardGiven the points T (5, 20°, 120°) to P (2, 80°, 30°): 1.) find the unit vector in cartesian coordinates at T that is directedtoward P. 2.) find the unit vector in spherical coordinates at T that is directedtoward P.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON