A long solenoid of radius a =10.0cm and length 15.0meters has N1 = 3500 turns and carries a clockwise, variable current; at time t=1.00sec, the current is 30.0 A, and at time t=3.00sec, the current is 6.00 A. Inside the solenoid is a small, circular coil having N2=55 turns, having a radius of b=7.00cm, having a resistance R=20.0 ohms, and whose plane makes a fixed angle of 25.0 degrees with respect to the long axis of the solenoid.
a. Find the magnetic field B in the solenoid at the times t=1.00sec, and t=3.00sec.
b. Find the average EMF induced in the small coil.
c. Find the average induced current in the small coil; is the direction of the induced current in the small coil clockwise or counterclockwise?