A flat coil with N turns, each of area A, is rotated at a constant angular speed ω about a diameter that lies in its plane. The rotation axis is perpendicular to a uniform magnetic field of magnitude B. The coil is connected to a load resistor of resistance R, and the total resistance of the coil itself is negligible. At time t=0 the normal to the plane of the coil is aligned with the magnetic field.
Ignore any effects of self-inductance.
(a) Derive an expression for the instantaneous emf E(t) induced in the coil as a function of time.
(b) Obtain the corresponding expression for the instantaneous current I(t) through the resistor.
(c) Determine the instantaneous electrical power P(t) delivered to the resistor and calculate its average value ⟨P⟩ over one full rotation of the coil.
(d) Compute the total electrical energy Erev delivered to the resistor during one complete revolution, and discuss how Erev depends on ω.