Macroscopic Electrodynamics Instructor's Solutions Guide

Walter Wilcox, Chris Thron

• Publisher: WSPC
• Year: 2016
• eBook ISBN: 9789814616676
• Topic: Physical Sciences
• Subtopic: Electromagnetism

This instructor's solutions guide accompanies our introductory graduate electrodynamics textbook, "Macroscopic Electrodynamics". We emphasize that this is a guide and not a step-by-step exposition for the 391 problems furnished in the text. Helpful indications of starting points and methods are given, as well as enough intermediate steps (and occasional final results) that a knowledgeable instructor can readily fill in the gaps. This approach is designed to provide the instructor with a powerful and time-saving teaching aid for introducing students to this beautiful and wide-ranging subject.

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This instructor's solutions guide accompanies our introductory graduate electrodynamics textbook, "Macroscopic Electrodynamics". We emphasize that this is a guide and not a step-by-step exposition for the 391 problems furnished in the text. Helpful indications of starting points and methods are given, as well as enough intermediate steps (and occasional final results) that a knowledgeable instructor can readily fill in the gaps. This approach is designed to provide the instructor with a powerful and time-saving teaching aid for introducing students to this beautiful and wide-ranging subject.

Request Inspection Copy

Chapter 1

Introduction and Perspectives

Guide to Exercise 1.1.1

(a)Three uses of the BAC–CAB rule from the vector identities subsection of Section 1.8 will do the job.

(b)Two uses of the basic differential chain rule for the gradient will suffice.

(c)Uses a first order differential identity for

from Section 1.8.

Guide to Exercise 1.1.2

The No-monopole and Faraday laws from Table 1.1 become identities. The changes to the Coulomb and Ampère-Maxwell equations are easily computed (see Eqs.(7.104) and (7.105)).

Guide to Exercise 1.1.3

Simply use the chain rule when taking the partial derivative of

with respect to t. The divergence of

uses a first order differential identity.

Guide to Exercise 1.4.1

(a)Use the Stokes law to change the contour integral into an area integral.

(b)The parametric representation of the ellipse is given by x = a cos θ, y = b sin θ. Substitute in the contour integral and integrate. Setting the result equal to the answer in (a) gives the area.

Guide to Exercise 1.4.2

(a)Use

in the Gauss theorem (see Integral identities), where

is an arbitrary constant vector.

(b)Use

in the Gauss theorem, where

is an arbitrary constant vector.

Guide to Exercise 1.4.3

Use

in the Stokes theorem (in Integral identities), where

is an arbitrary constant vector.

Guide to Exercise 1.5.1

(a)Specializing the Gauss theorem to two dimensions and using

for an infinite line charge in three dimensions or

for a point charge in two dimensions, Table 1.6 gives the radial dependence E_r = 2Q/r or E_r = Q/r in the two cases, respectively.

(b)One may work with the Stokes theorem in the form

and show that 1)

where

(P, Q arbitrary) and

is the outer normal, and that 2)

.

Chapter 2

Introduction to Electrostatics

Guide to Exercise 2.1.1

(a)Naïvely,

(b)One may use index notation with

and Summation...

Table of contents

• Cover page
• Title page
• Copyright page
• Preface
• Contents
• 1. Introduction and Perspectives
• 2. Introduction to Electrostatics
• 3. Boundary Value Problems in Electrostatics
• 4. Electrostatics in Cylindrical and Spherical Coordinates
• 5. Multipoles, Electrostatics of Macroscopic Media, Dielectrics
• 6. Magnetostatics
• 7. Time Varying Fields I
• 8. Time Varying Fields II
• 9. Plane Electromagnetic Waves and Propagation in Matter
• 10. Waveguides and Resonant Cavities
• 11. Radiation of Systems and Point Paricles
• 12. Scattering and Diffraction
• 13. Relativistic Formulations of Electrodynamics
• 14. Special Topics
• 15. Appendix