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N turns are tightly wound to form a spiral plane of outer radius a. If the magnetic induction B=B0 sin ωt varies perpendicular to the plane of spiral,then the the emf induced in the spiral coil is

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a

πa2B0ωNcosωt2

b

πa2B0Nωcosωt4

c

πa2B0Nωcosωt

d

πa2B0Nωcosωt3

answer is D.

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Detailed Solution

Let the hypothetical elementary loop have radius x. Then emf induced in this loop dε=AdBdt=πx2B0cosωt dN=πx2B0ωcosωt(Na)dx or ε=∫0aB0πωNacosωtx2dx=πa2B0ωNcosωt3

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