Neco 2021 Physics Question 5

A rectangular single‑turn loop of wire has length \(l = 0.50\ \text{m}\) and width \(w = 0.20\ \text{m}\). It rotates with a constant angular speed \(\omega = 50\ \text{rad s}^{-1}\) in a uniform magnetic field of magnitude \(B = 0.30\ \text{T}\), the axis of rotation being perpendicular to the field. The loop has a resistance of \(R = 2.0\ \Omega\). (a) Write the expression for the instantaneous induced emf in the loop and give its maximum value. (b) If the loop is connected to an external resistor \(R_{L}\), determine the value of \(R_{L}\) that will make the power delivered to \(R_{L}\) maximum. (c) Calculate this maximum power (in watts) delivered to the load resistor. Give your answer to two decimal places.