A flat rectangular coil of 50 turns, each of area 25 cm², is initially at rest in a uniform 0.20 T magnetic field. The magnetic field is directed perpendicular to the plane of the coil at t=0. Beginning at that instant, the coil is subjected to a constant angular acceleration of 15rad/s2 about an axis that lies in the plane of the coil and passes through its center.
The coil is part of a closed circuit whose total resistance is 12 Ω.
(a) Derive an expression for the angular displacement of the coil as a function of time during the interval in which the angular acceleration is constant.
(b) Using your result from part (a), obtain an expression for the magnetic flux through the coil as a function of time.
(c) Hence derive an expression for the induced emf as a function of time for t>0 while the angular acceleration remains constant.
(d) Calculate the magnitude of the induced emf at t=0.40s.
(e) Determine the instantaneous power dissipated as thermal energy in the circuit at t=0.40s. Assume the resistance remains constant.