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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=BAcos⁡θ=πr2Bcos⁡ωt∴ ε=−dϕdt=πr2Bω sin⁡ωt∴  i=εR=πr2Bω sin⁡ωt2πr.λ=rBω2λsin⁡ωt∴ Im=rBω2λ and Irms=Im2=0.05×1×102×2×2 A=182 A
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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