Q.

Figure shows three regions of magnetic field each of area A, and in each region, magnitude of magnetic field decreases at a constant rate α.It E→ is the induced electric field, then the value of the line integral ∮  E→⋅dr→ along the given loop is equal to

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a

αA

b

−αA

c

3αA

d

−3αA

answer is B.

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Detailed Solution

As anticlockwise direction is positive, so area vector out wards is positive. So net flux through the given loop isϕ=−BA−BA+BA=−BA∮  E→⋅dr→=−dϕdt=−d(−BA)dt=AdBdt=A(−α)⇒ ∮  E→⋅dr→=−αA
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