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 30 - Electromagnetic Induction - Exercises and Problems - Page 870: 15


The magnetic field strength is increasing. $\frac{\Delta B}{\Delta t} = 2.3~T/s$

Work Step by Step

If the magnetic field directed into the page is increasing, there is more magnetic flux going through the loop. By Lenz's law, a current is induced around the loop which opposes the change in flux. Then, the current must produce a magnetic flux directed out of the page. By the right hand rule, this current flows counter-clockwise around the loop. Since the current flows counter-clockwise around the loop, we can conclude that the magnetic field strength is increasing. We can find the induced $emf$: $emf = I~R$ $emf = (0.150~A)(0.10~\Omega)$ $emf = 0.015~V$ We can find $\frac{\Delta B}{\Delta t}$: $emf = \frac{d\phi}{dt}$ $emf = \frac{\Delta B~A}{\Delta t}$ $\frac{\Delta B}{\Delta t} = \frac{emf}{A}$ $\frac{\Delta B}{\Delta t} = \frac{0.015~V}{(0.080~m)^2}$ $\frac{\Delta B}{\Delta t} = 2.3~T/s$
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