文档介绍：INSTRUCTOR'S
SOLUTIONS
MANUAL
INTRODUCTION to
ELECTRODYNAMICS
Third Edition
David J. Griffiths
TABLE OF CONTENTS
Chapter 1 Vector Analysis 1
Chapter 2 Electrostatics 22
Chapter 3 Special Techniques 42
Chapter 4 Electrostatic Fields in Matter 73
Chapter 5 ostatics 89
Chapter 6 ostatic Fields in Matter 113
Chapter 7 Electrod ynamics 125
Chapter 8 Conservation Laws 146
Chapter 9 ic Waves 157
Chapter 10 Potentials and Fields 179
Chapter 11 Radiation 195
Chapter 12 Electrodynamics and Relativity 219
Chapter 1
Vector Analysis
Problem
(a) From the diagram, IB + CI COSO3= IBI COSO1+ ICI COSO2'Multiply by IAI.
IAIIB + CI COSO3= IAIIBI COSO1 + IAIICI COSO2. ICI sin 82
So: A.(B + C) = + . (Dot product is distributive.)
Similarly: IB + CI sin 03 = IBI sin 01 + ICI sin O2, Mulitply by IAI n.
IAIIB + CI sin 03n = IAIIBI sin 01n + IAIICI sin O2n. IBlsin81
If n is the unit vector pointing out of the page, it follows that A
Ax(B + e) = (AxB) + (Axe). (Cross product is distributive.)
(b) For the general case, see G. E. Hay's Vector and Tensor Analysis, Chapter 1, Section 7 (dot product) and
Section 8 (cross product).
Problem
The triple cross-product is not in general associative. For example,
suppose A = ~ and C is perpendicular to A, as in the diagram.
Then (B XC) points out-of-the-page, and A X(B XC) points down, k-hB
and has magnitude ABC. But (AxB) = 0, so (Ax B) xC = 0 :f.
Ax(BxC). BxC iAx(Bxe)
Problem z
A = + 1x + 1Y- H; A = /3; B = 1x + 1Y+ Hi B = /3.
= +1 + 1-1 = 1 = ABcosO = /3/3coso =>cosO= ~.
y
10 = COS-1(t) ~ ° I
x
Problem
The cross-product of any two vectors in the plane will give a vector perpendicular to the plane. For example,
we might pick the base (A) and the left side (B):
A = -1 x + 2 y + 0 z; B = -1 x + 0 Y + 3 z.
1
2 CHAPTER 1. VECTOR ANALYSIS
x y Z
AxB = I -1 2 0 1= 6x + 3y + 2z.
-1 0 3
This has the' right direction, but the wrong magnitude. To make a