Nonstandard RL circuit

A thin ring with resistance R=10 ΩR=10~\Omega and self inductance L=0.2 HL=0.2~\mbox{H} rotates with constant angular speed ω=100 rad/s \omega=100~\mbox{rad/s} in an external uniform magnetic field perpendicular to the rotation axis. As a result, the magnetic flux created by the external field varies with time as Φ(t)=Φ0cos(ωt)whereΦ0=0.1 Wb. \Phi(t)=\Phi_{0}\cos(\omega t) \quad \textrm{where} \quad \Phi_{0}=0.1~\mbox{Wb} . Because of the resistance of the ring, energy is being continuously dissipated in the system. What average power Pˉ\bar{P} in Watts must develop the external forces to keep the ring rotating at constant angular speed ω\omega (on average).

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