A circular conducting coil of 200 turns, each of radius 5.0 cm, is placed in a region where a uniform 0.30 T magnetic field is directed perpendicular to the axis of rotation of the coil. The coil is set into steady rotation at 1 200 rev/min about a diameter that lies in the plane of the coil. The coil’s internal resistance is negligible.
Take the instant t=0 to be the moment when the normal to the plane of the coil is exactly aligned with the magnetic field.
(a) Determine the magnetic flux through the coil at t=0.
(b) Write an expression for the magnetic flux through the coil as a function of time.
(c) Derive an expression for the induced emf as a function of time.
(d) Calculate the numerical value of the maximum (peak) induced emf.
(e) Determine the instantaneous emf at t=6.0×10−3s. State its sign (positive or negative) relative to the sense defined by the coil’s rotation.