Example 7.7. A uniform magnetic field B(1), pointing straight up, fills theshaded circular region of Fig. 7.25. If B is changing with time, what is the in-duced electric field?SolutionE points in the circumferential direction, just like the magnetic field inside a longstraight wire carrying a uniform current density. Draw an Amperian loop of radiuss, and apply Faraday's law:doE-d1 = E(27s) =(s²B(1))=-7S2 dBdidtTherefores dBE2 drIf B is increasing, E runs clockwise, as viewed from above.13 Magnetostatics holds only for time-independent currents, but there is no such restriction on 3B/ar.Chapter 7 ElectrodynamicsB(1)EAmperian loopFIGURE 7.25dtRotationdirectiondlλFIGURE 7.26

Changing magnetic field induces electric field according to Faraday's law. In the question, its…

Answered: Example 7.7. A uniform magnetic field…

Example 7.7. A uniform magnetic field B(1), pointing straight up, fills the shaded circular region of Fig. 7.25. If B is changing with time, what is the in- duced electric field?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Example 7.7. A uniform magnetic field B(1), pointing straight up, fills the
shaded circular region of Fig. 7.25. If B is changing with time, what is the in-
duced electric field?
Solution
E points in the circumferential direction, just like the magnetic field inside a long
straight wire carrying a uniform current density. Draw an Amperian loop of radius
s, and apply Faraday's law:
do
E-d1 = E(27s) =
(s²B(1))
=-7S
2 dB
di
dt
Therefore
s dB
E
2 dr
If B is increasing, E runs clockwise, as viewed from above.
13 Magnetostatics holds only for time-independent currents, but there is no such restriction on 3B/ar.
Chapter 7 Electrodynamics
B(1)
E
Amperian loop
FIGURE 7.25
dt
Rotation
direction
dl
λ
FIGURE 7.26

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