2. (36 pts) A circular circuit forms a loop of radius a and resistance R, 1s centered inside a long solenoid concentrically, so they both share the same center axis. The circular loop has a time- varying voltage source with voltage V(t) = V, sin wt connected to it, producing a current in the loop. The solenoid has radius s, and with n coils per meter, and the ends of the solenoid wires are attached in a closed circuit with resistance R. a. b. (10pts) Find the EMF induced in the solenoid (for Part a, assume any \"back EMF\" 1n the circular loop is negligible). (10 pts) Determine the approximate \"back EMF\" , in the circular loop by finding the EMF generated in the circular loop due to the current induced in the solenoid (from part a). (8 pts) In the approximation in part b, the total EMF around the circular loop is now composed of the EMF from the voltage source V (t) and the back EMF: Vtotci'rcle = V(t) + 8b Show, for reasonable values of a, Ry, V), w, so, n, R (that is, values that could be produced in a simple lab, e.g. a = 1cm), that the amplitude V;, of the voltage source is much greater than the amplitude of the back EMF &,,. (8 pts) If the frequency w were increased, but V/; remained fixed, would the current in the circular loop increase, decrease or stay the same? Explain using physics principles. Assume the self inductance of the loop is negligible