Q.

The magnetic field of an electromagnetic wave obeys the relation in a certain region is B=10−12sin(1×106t) in tesla, where 't'is the time. Then, the induced emf, in a 100 turns in coil of area 10cm2 oriented perpendicular to the field is

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a

−2×10−7cos(1×106t)V

b

−1×10−7cos(1×106t)V

c

−1.5×10−7cos(1×106t)V

d

−3×10−7cos(1×106t)V

answer is B.

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Detailed Solution

Induced emf  e=−dϕdt=−Nd(BAcosθ)dt     [here θ=0o  as field is normal to coil] ⇒e=-NAd(B)dt ⇒e=-NAd(Bosinωt)dt ⇒e=-NABoωcosωt ⇒e=-100×10×10-4×10-12×106 cos(106t) ⇒e=-10-7 cos(106t)
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