# Nonstandard RL circuit

**Electricity and Magnetism**Level 3

A thin ring with resistance \(R=10~\Omega\) and self inductance \(L=0.2~\mbox{H}\) rotates with constant angular speed \( \omega=100~\mbox{rad/s}\) 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
\[ \Phi(t)=\Phi_{0}\cos(\omega t) \quad \textrm{where} \quad \Phi_{0}=0.1~\mbox{Wb} .\]
Because of the resistance of the ring, energy is being continuously dissipated in the system. What average power \(\bar{P}\) **in Watts** must develop the external forces to keep the ring rotating at constant angular speed \(\omega\) (on average).