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?

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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
Transcribed Image Text: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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