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Magnetic flux and induced emf

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Question

A uniform magnetic field B = 0.5 T exists in a circular region of radius R = 5 m. A loop of radius R = 5 m encloses the magnetic field at t = 0 and then pulled at uniform speed v = 2 ms-1 in the plane of the paper. Find the induced emf (in V) in the loop at time t = 3 s.

Moderate
Solution

O1M=vt-R+2R-vt2=v2

l=PN=2R2-O1M22R2-vt22=4R2-v2t2

so E=Bvl=Bv4R2-v2t2

given R=5m, v=2m/s, t = 3s

E=0.5×24×25-4×9=8V


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