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Questions  

 N turns are tightly wound to form a spiral plane of outer radius a. If the magnetic induction B=B0sinωt varies perpendicular to the plane of spiral,then the the emf induced in the spiral coil is

a
πa2B0ωNcosωt2
b
πa2B0Nωcosωt4
c
πa2B0Nωcosωt
d
πa2B0Nωcosωt3

detailed solution

Correct option is D

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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