Gce Model Questions Vol1 2017 Physics Question 6

A rectangular coil of N = 200 turns and area A = 0.020\,m^{2} rotates uniformly in a uniform magnetic field of magnitude B = 0.5\,T. The coil has an internal resistance of 5\,\Omega and is connected to an external resistor. The peak induced emf in the coil is given by \(\varepsilon = N B A \omega\), where \(\omega\) is the angular speed in rad\,s^{-1}.\n\n(i) Determine the angular speed \(\omega\) (to two decimal places) required so that, when the external resistor is chosen to maximise the instantaneous power transferred to it, the maximum power is 2.0\,W.\n\n(ii) If the coil is then rotated at half this angular speed, what is the greatest instantaneous power that can be delivered to any external resistor? Give your answer to two decimal places in watts.