Chapter 8.2, Problem 1dT

Three loops, all made of the same type of wire, are placed near the ends of identical solenoids as shown. The solenoids are connected in series. Assume that the magnetic field near the end of each of the solenoids is uniform.
 
LOOP 2 consists of two turns of a single wire that is twice as long as the wire used to make loop 1. Loop 3 is made of a single wire that is half as long as the wire used to make loop 1.
 
Just after the switch has been closed, the current through the battery begins to increase. The following questions concern the period of time during which the current is increasing.
 
1. Let $\epsilon$ represent the induced emf of loop 1. Find the induced emf in each of the other loops in terms of E. Explainyour reasoning.
 
2. Let R represent the resistance of loop 1. Find the resistance of each of the other loops in terms of R. Explain.

3. Find the current induced through the wire of each of the loops in terms of E and R.