1. For a long solenoid, we discovered in a problem-of-the-day that B = µ,nl, where n is the number of turns of wire per unit length along the solenoid. a. Use this fact and Faraday's Law of induction to calculate the inductance of a solenoid of cross-sectional area A and length I. b. If a solenoid has 10ʻ turns per meter, and is 5 cm in diameter and 50 cm long, and is carrying a current of 10 A which is turned off in a time of 0.001 sec, what is the induced "back voltage" developed?

4.) In the circuit shown, the initial voltage across the 10 microFarad capacitor is 12V.  The solenoid has an inductance of 0.7 H. There is no resistance. a) Find the charge on the capacitor 1.0 millisecond after the switch S is closed. b) At what time will the current in the solenoid reach its maximum value? c) What is the maximum energy stored in the magnetic field of the solenoid?

c1. What is the magnitude of the induced emf at t = 0 s? c2. What is the magnitude of the induced emf after a long time has passed? d. After the current in the RL circuit has reached its final value (as in b2. above) the positions of the switches are reversed, with S1 open and S2.How long does it take for the current to reach a tenth of its initial value?

2. The current in a very long solenoid with radius a and n turns per unit length varies over time as i(t) = Ct². Concentric with the solenoid is a conducting ring of radius r. a) Write an expression for the potential difference induced in the ring. b) Write an expression for the magnitude of the electric field induced at an arbitrary point on the ring. c) Is the ring necessary for the induced electric field to exist? Radius = r Radius i(t) = Ct² -O V = V(t) = a

4. In the middle of the selenoid with a diameter of D = 2 cm, length L= 20 cm and consisting of N1 = 1200 turns there is a small coil with a diameter of d = 1 cm. The length of this small coil is l= 2 cm and consists of N2 = 50 turns a. Calculate the mutual inductance between the coils. b. If the current in the şelenoid changes at a rate of 0.5 A / s, calculate the emf induced ɛ on the small coil.