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

Question

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

Infinity Learn · Accepted Answer

At any time t, ϕ$$=BAcos$$⁡θ$$=$$π$$r2Bcos$$⁡ωt∴ ε$$=$$−dϕ$$dt=$$π$$r2B$$ω $$sin$$⁡ωt∴  $$i=$$ε$$R=$$π$$r2B$$ω $$sin$$⁡ω$$t2$$$$π$$r.λ$$=rB$$ω$$2$$λ$$sin$$⁡ωt∴ $$Im=rB$$ω$$2$$λ and $$Irms=Im2=0.05$$×$$1$$×$$102$$×$$2$$×$$2$$ $$A=182$$ A

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