Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 1.1, Problem 1.10P
(a)
To determine
The transformation of components of a vector under translation of coordinates.
(b)
To determine
The transformation of components of a vector under inversion of coordinates.
(c)
To determine
The transformation of components of a cross product under inversion.
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Fig. 1
A (2.80 cm)
60.0°
60.0°
B (1.90 cm)
1.
1. Fig. I shows the two vectors A and B.
(a) Find the scalar product à B and the magnitudes and directions of the vector
products Ă x B and B x A using vector dot and cross product definition and
rules. Do not use unit vectors.
(b) Write Á and B in unit vector notation and using them determine the scalar
product à · B and the vector produets à x B and B xà again. Compare your
results in part l(a) and 1(b).
Vector A has magnitude 5.00 m and lies in the xy-plane in adirection 53.0o from the +x-axis axis measured toward the +y-axis.Vector b has magnitude 8.00 m and a direction you can adjust. (a) Youwant the vector product A : B to have a positive z-component of thelargest possible magnitude. What direction should you select for vectorB S? (b) What is the direction of B for which A : B has the mostnegative z-component? (c) What are the two directions of B S for whichA : B is zero?
The vector product of two vectors A and B is a vector and so has both a magnitude and direction:
1. Magnitude: The magnitude of the vector product Ax Bis:
||A × B|| = |A|| ||B|| sin e = AB₁ = A₁B
where is the angle between the vectors. Here B₁ = B sin 6 is the component of B
perpendicular to A while A₁ = A sine is the component of A perpendicular to B.
Special Cases: Give answers to questions below in terms of the magnitudes A and B.
What is Ax B if A and Bare parallel?
If A and Bare perpendicular?
2. Direction: The direction of the vector product Ax B is perpendicular to the plane determined by the vectors A
and B, and follows a "right hand rule". This "right hand rule" is different from the one we used to determine
angular velocity. The steps to determining the direction of the vector product are
a. Determine the two possible directions: First determine the only two possible directions that are perpendicular
to both A and B. The vector product must be in one of these two directions.…
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
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