A thin non-conducting ring of mass m , radius a, carrying a charge q can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest and no magnetic field was present. At instant t = 0, a uniform magnetic field is switched on which is vertically downwards and increase with time according to the law B=B0t . Neglecting magnetism induced due to rotational motion of the ring. The angular acceleration of the ring as seen from above is B0qxm , then x is______
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answer is 2.
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Detailed Solution
Sudden appearance of B produces non conservative E.E2πa=E=dφdt=AdBdt=AdB0tdt⇒E2πa=πa2B0⇒E=aB02This electric field acts tangentially to ring.Torque=τ=Fa=qEa=qaB02a⇒Iα=qa2B02⇒ma2α=qa2B02⇒α=qB02m