Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 31 - Electromagnetic Fields and Waves - Stop to Think 31.1 - Page 881: 1


Option b.

Work Step by Step

Recall that the Galilean transformation equations are: $\displaystyle \vec{E}_B = \vec{E}_A + \vec{v} \times \vec{B}_A$ $\displaystyle \vec{B}_B = \vec{B}_A - \frac{1}{c^2}\vec{v} \times \vec{E}_A$ In the diagram shown, the electric field is in the +$\hat k$ direction and the magnetic field is in the +$\hat i$ direction. The direction of the velocity of reference frame B is also in the +$\hat i$ direction. All we have to do is plug the unit vectors into the Galilean transformation equations to find the directions of the vectors in reference frame B. $\vec{E}_B = \hat k + [(+\hat i) \times (+\hat i)] = \hat k + 0 = \hat k$ $\vec{B}_B = \hat i - [(+\hat i) \times (+\hat k)] = \hat i - (-\hat j) = \hat i + \hat j$ Therefore, the diagram for reference frame B must have an electric field pointing in the positive $z$ direction (+$\hat k$) and have a magnetic field pointing in both the positive $x$ and $y$ directions ($\hat i + \hat j$). The only diagram that has this is option b. Option b. is correct.
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