First slide
Magnetic flux and induced emf
Question

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   Edr along the given loop is equal to

Moderate
Solution

As anticlockwise direction is positive, so area vector out wards is positive. So net flux through the given loop is

ϕ=BABA+BA=BA  Edr=dϕdt=d(BA)dt=AdBdt=A(α)   Edr=αA

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