A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the inducedelectric field at point P at a distance r from the center of the circular region
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a
is zero
b
decreases as 1/r
c
increases as r
d
decreases as 1/r2
answer is B.
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Detailed Solution
Construct a concentric circle of radius r. The induced electric field (E) at any point on the circle is equal to that at P.For this circle∮ E→.dl→=dφdt=AdBdt⇒ E×(2πr)=πa2⋅dBdt⇒E=a22rdBdt⇒E∝1r