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A magnetic field B is confined to a region `r le` a and points out of the paper (the z-axis), r = 0 being the centre of the cicular region. A charged ring (charge = Q) of radius b,bgt a and mass m lie in the x-y plane with its centre at origin. The ring is free to rotate and is at rest. The magnetic field is brougth to zero in time `Delta t`. Find the angular velocity `omega or the ring after the field vanishes.A. `(qBa^(2))/(2mb)`B. `(qBa)/(2mb^(2))`C. `(2b^(2))/(qBa^(2))`D. `(qb^(2))/(2Ba^(2))` |
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Answer» Correct Answer - D Let E is the electric field generated around the charged ring of radius of b, then, `epsi=(dphi)/(dt)` `ointvec(E)*dvec(l)=(Bpia^(2))/(Deltat)` `or Eb=(Ba^(2))/(2(Deltat))" n "......(i)` Torque acting on the ring `tau=bxx"forces"=bqE` `=(qBa^(2))/(2(Deltat)) " "` [ Using (i)] If `DeltaL` is change in angular momentum of the chorged ring, then, `tau=(DeltaL)/(Deltat)=(L_(2)-L_(1))/(Deltat)` `:. L_(2)-L_(1)=tau(Deltat)` `=(qBa^(2)Deltat)/(2Deltat)=(qBa^(2))/(2)` As initial angular momentum, `L_(1)=0` `:. L_(2)=(qBa^(2))/(2)=I omega=mb^(2)omega :. omega=(qBa^(2))/(2mb^(2))` |
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