A ring of mass 4 kg is uniformly charged with λ = 4 c / m and kept on rough horizontal surface with friction coefficient μ = 4 π . A time varying magnetic field B = B 0 t 2 is applied in a circula

Question

A ring of mass 4 kg is uniformly charged with $λ = 4 c / m$ and kept on rough horizontal surface with friction coefficient $μ = \frac{π}{4}$ . A time varying magnetic field $B = B_{0} t^{2}$ is applied in a circular region of radius $a (a > r)$ perpendicular to the plane of ring as shown in figure. Find out the time when ring just start to rotate on surface. (take $a = 5 cm$ and $g = 10 m / s^{2}, B_{0} = 125 S I$ units)

TestHub · Accepted Answer

Induced electric field E ( 2 π r ) = d t d ϕ ​ E = 2 π r π a 2 2 B 0 ​ t ​ Torque due to field about centre of ring τ 1 ​ = ( qE ) r = [ λ ( 2 π r )] ( 2 π r 2 π a 2 B 0 ​ t ​ ) r Ring starts rotating when τ due to electric field = τ due to friction. τ 1 ​ τ 1 ​ = ( μ m g ) r Solving t = 2 π a 2 B 0 ​ λ μ m g ​ = 4 s

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