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Q.

The magnetic field of an electromagnetic wave , obeys the relation in a certain region , is  B=10−12sin(5×106t)T, where t is the time . Then the induced  emf, in a 300 turns coil of area 20cm2 oriented perpendicular to the field is

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a

−2×10−5cos(5×106t)V

b

−3×10−6cos(5×106t)V

c

−2.5×10−6cos(5×106t)V

d

−3.3×10−6cos(5×106t)V

answer is B.

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Detailed Solution

Induced   emf  : e=−dϕdt=−Nd(BAcosθ)dt ⇒e=-NAdBdt        [Coil is perpendicular to field ∴cosθ = 1] ⇒e=-NAd(Bosinωt)dt ⇒e=−BoANωcosωt ⇒e= −10−12×20×10−4×3×102×5×106cos(5×106t) ⇒e=-3×10-6cos(5×106t)
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The magnetic field of an electromagnetic wave , obeys the relation in a certain region , is  B=10−12sin(5×106t)T, where t is the time . Then the induced  emf, in a 300 turns coil of area 20cm2 oriented perpendicular to the field is