Problem 4: Inductor in a Changing Magnetic Field [30 points]
An inductor is formed by winding N turns of a thin conducting wire into a circular loop of radius a. The inductor loop is in the x-y plane with its center at the origin and connected to a resistor as shown in the figure. In the presence of a magnetic field B = Bo2ay + 3azsint a, find:
a) The magnetic flux linking a single turn of the inductor.
b) The transformer emf, given that N = 10, Bo = 0.2 T, a = 10 cm, and ω = 103 rad/s.
c) The polarity of Vemf at t = 0.
d) The induced current in the circuit for R = 1 K, assuming negligible wire resistance.
Vemf: Voltage induced in the inductor
N turns: Number of turns in the inductor