Q.

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 induced electric field at point P at a distance r from the centre of the circular region

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a

Is zero

b

Decreases with increase in r

c

Increases with increase in r

d

Decreases with decrease in r

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 or E×(2πr)=πa2⋅dBdt⇒E=a22rdBdt⇒E∝1r
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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 induced electric field at point P at a distance r from the centre of the circular region