In this problem, you derive the expression for the self-inductance of a long solenoid [Eq. (20-30)]. The solenoid has n turns per unit length, length ℓ, and radius r. Assume that the current flowing in the solenoid is I. 

(a) Write an expression for the magnetic field inside the solenoid in terms of n, ℓ, r, I, and universal constants. 

(b) Assume that all of the field lines cut through each turn of the solenoid. In other words,assume the field is uniform right out to the ends of the solenoid—a good approximation if the solenoid is tightly wound and sufficiently long. Write an expression for the magnetic flux through one turn. 

(c) What is the total flux linkage through all turns of the solenoid? 

(d) Use the definition of self-inductance [Eq. (20-27)] to find the selfinductance of the solenoid.

L= = Hon 3