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Q.

A ring of mass 4 kg is uniformly charged with  λ = 4 Cm-1 and kept on rough horizontal Surface with  friction Coefficient μ=π4. A time varying magnetic    field B = B0t2 is applied in  a  circular region of radius  aa < r perpendicular to the plane of ring as shown in figure.

Find out the time(in seconds)  when ring just starts to rotate on  surface. Take  a = 5cm and  g=10ms-2B0=125 SI unit.

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answer is 4.

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Detailed Solution

Induced electric  field

 E(2πr)=dϕdt E=πa22B0t2πr

Torque due to field about centre of ring

τ1=qEr=λ2πr2πa2B0t2πrr

Ring starts rotating when  τdue to electric field=τdue to friction  

τ1=μmgr 

Solving, we get  t=μmg2πa2B0λ=4 s

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