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 R, as shown in Fig. 6-3. In the presence of a magnetic field B=B_(0)(hat (y)2+hat (z)3)sinomega t where a is the angular frequency, find (a) the magnetic flux linking a single turn of the inductor, (b) the transformer emf given that N=10, B_(0)=0.2T, a=10cm and omega =10^3rad/s (c) the polarity of V_(cmf)^tr at t=0 and (d) the induced current in the circuit for R=1kOmega (assume the wire resistance to be much smaller than R)

(a) The magnetic flux linking a single turn of the inductor is given by: where is the magnetic field strength, is the area of the loop, and is the angular frequency.(b) The transformer emf is given by: Substituting the expression for from part (a), we get: (c) The polarity of at can be determined by substituting into the expression for from part (b). Since is zero at , the emf is also zero at that time. Therefore, the polarity of at is indeterminate.(d) The induced current in the circuit can be found using Ohm's law: Substituting the expression for from part (b), we get: Substituting the given values, we get: Simplifying further, we get: Therefore, the induced current in the circuit is A.