An alternating current I(t)=I0cos(ωt) (amplitude 0.5 A, frequency 60 Hz) flows down a straight wire, which runs along the axis of a toroidal coil with rectangular cross section (inner radius 1 cm, outer radius 2 cm, height 1 cm, 1000 turns). The coil is connected to a 500 Ω resistor.
(a) In the quasistatic approximation, what emf is induced in the toroid? Find the current, IR(t), in the resistor.
(b) Calculate the back emf in the coil, due to the current IR(t). What is the ratio of the amplitudes of this back emf and the ``direct'' emf in (a)?