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32-3 Induced Magnetic Fields
Faraday's law of induction in the form
Electric field induced along a closed loop by the changing magnetic flux
B encircled by the loop.Can a changing electric flux induce a magnetic field?
Yes it can Maxwell's equation governing the induction of a magnetic field is almost symmetric with Eq. 32-2.
Magnetic field induced along a closed loop by the changing electric flux
E the region encircled by loop.As an example of this sort of induction with the charging of a parallel- plate capacitor with circular plates Fig.
32-5.
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FIG.32·5 (a) circular parallel- plate capacitor, shown in side view, is being charged by a constant current i.
FIG.32·5 (b) view from within the capacitor, looking toward the plate at the right in (a).
The electric field uniform directed into the page
(toward the plate), and grows in magnitude as the charge on the capacitor increases.
The magnetic field induced by this changing electric field shown at four points on a circle with a radius r less than the plate radius R.
Consider a circular loop concentric with the capacitor
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plates and has a radius smaller than that of the plates through point 1 in Figs. 32-5a b
Electric field through this loop change changing
electric flux induces a magnetic field around the loop experiment proves that
Consider a larger loop through point 2 outside the plates in Figs. 32-5a and b a magnetic field is induced around that loop
Changing electric field induced magnetic fields between the plates both inside and outside the gap Changing electric field stop induced magnetic fields disappear
Eq. 32-3 similar to Eq. 32-2 they differ in two ways.
First Eq. 32-3 the symbols μo
o but they appear only because employ SI units.Second Eq. 32-3 lacks the minus sign of Eq. 32-2 the induced electric field E the induced magnetic field B have opposite directions when they are produced in
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otherwise similar situations.
Fig. 32-6 shows this opposition
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Ampere-Maxwell Law
Ampere's law similar to Eq. 32-3
ienc is the current encircled by the closed loop
Combine Eq. 32-3 and Eq. 32-4 into the single equation
When there a current but no change in electric flux the first term on the right side of Eq. 32-5 zero Eq. 32-5 reduces to Eq. 32-4 Ampere's law
When there a change in electric flux but no current the second term on the right side of Eq.
32-5 zero Eq. 32-5 reduces to Eq. 32-3 Maxwell's law of induction.
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Ans: a, c, b, d (zero)
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