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Instructor’s Solution Manual Introduction to Electrodynamics Fourth Edition David J. Griffiths
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Instructor’s Solution ManualIntroduction to Electrodynamics
Fourth Edition
David J. Griffiths
2014
,Contents
1 Vector Analysis 4
2 Electrostatics 26
3 Potential 53
4 Electric Fields in Matter 92
5 Magnetostatics 110
6 Magnetic Fields in Matter 133
7 Electrodynamics 145
8 Conservation Laws 168
9 Electromagnetic Waves 185
10 Potentials and Fields 210
11 Radiation 231
12 Electrodynamics and Relativity 262
,Preface
Although I wrote these solutions, much of the typesetting was done by Jonah Gollub, Christopher Lee, and
James Terwilliger (any mistakes are, of course, entirely their fault). Chris also did many of the figures, and I
would like to thank him particularly for all his help. If you find errors, please let me know (griffith@reed.edu).
David Griffiths
, Chapter 1
Vector Analysis
Problem 1.1
✒
✣
}
(a) From the diagram, |B + C| cos ✓3 = |B| cos ✓1 + |C| cos ✓2 . Multiply by |A|.
|A||B + C| cos ✓3 = |A||B| cos ✓1 + |A||C| cos ✓2 . |C| sin θ2
So: A·(B + C) = A·B + A·C. (Dot product is distributive)
θ2
Similarly: |B + C| sin ✓3 = |B| sin ✓1 + |C| sin ✓2 . Mulitply by |A| n̂. θ3 ✯
|A||B + C | sin ✓3 n̂ = |A||B| sin ✓1 n̂ + |A|| C| sin ✓2 n̂.
If ˆn is the unit vector pointing out of the page, it follows that `
θ1
˛¸ x` ˛¸ x
} ✲A|B| sin θ
1
|B| cos θ1 |C| cos θ2
A⇥(B + C) = (A⇥B) + (A⇥C). (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 1.2 C
✻
The triple cross-product is not in general associative. For example,
suppose A = B and C is perpendicular to A, as in the diagram. ✲A=B
Then (B⇥C) points out-of-the-page, and A⇥(B⇥C) points down, ❂
and has magnitude ABC. But (A⇥B) = 0, so (A⇥B)⇥C = 0 6=
B×C ❄
A×(B×C)
A⇥(B⇥C).
Problem 1.3 z✻
p p
A = +1 x̂ + 1 ŷ — 1 ẑ; A =
3; B = 1 x̂ + 1 ŷ + 1 ẑ; B = 3.
p p ✣B
A·B = +1 + 1 — 1 = 1 = AB cos ✓ = 3 3 cos ✓ ) cos ✓ = 1 .3
θ
✲y
1
✓= cos— 1 3 ⇡ 70.5288 ❲
○
✰ A
x
Problem 1.4
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 x̂ + 2 ŷ + 0 ẑ; B = —1 x̂ + 0 ŷ + 3 ẑ.
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