A thin metallic ring of radius 5 cm is made of a wire of resistance 2 Ωm. The ring is placed in a uniform magnetic field of induction 1 Tesla with its plane perpendicular to the field. Now the ring starts rotating with angular velocity ω=10 rad/sec. Then rms value of current induced in the ring is
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a
142 A
b
182 A
c
122 A
d
42 A
answer is B.
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Detailed Solution
At any time t, ϕ=BAcosθ=πr2Bcosωt∴ ε=−dϕdt=πr2Bω sinωt∴ i=εR=πr2Bω sinωt2πr.λ=rBω2λsinωt∴ Im=rBω2λ and Irms=Im2=0.05×1×102×2×2 A=182 A