University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 29 - Electromagnetic Induction - Problems - Exercises - Page 984: 29.32


a. Clockwise. b. 26.3m/s.

Work Step by Step

a. The magnetic flux through the loop is increasing. The field is out of the page and the flux is increasing. By Lenz’s Law, the field caused by the induced current is directed to oppose the change in flux. The induced current makes a field that is directed into the page, to fight the increasing flux. By the right hand rule, the induced current is clockwise. b. The motional emf is vBL. Divide emf by the resistance to find the current. $$I=\frac{vBL}{R}$$ The force is given by $ILB$. $$F=\frac{vBL}{R}LB $$ The rate at which this force does work is Fv. $$P=Fv=\frac{v^2B^2L^2}{R}$$ Solve for the speed, v. $$ v=\frac{\sqrt{PR}}{BL} $$ $$ v=\frac{\sqrt{(0.840W)(45.0\Omega)}}{(0.650T)(0.360m)}=26.3m/s $$
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