In this problem, you derive the expression for the self-inductanceof a long solenoid

[L = Âµ0n2pr2script i].

The solenoid has n turns per unit length, length script i, andradius r. Assume that the current flowing in the solenoid isI.

(a) Write an expression for the magnetic field inside the solenoidin terms of n, script i, r, I, and universal constants.

B = _________________

(b) Assume that all of the field lines cut through each turn of thesolenoid. In other words, assume the field is uniform right out tothe ends of the solenoidâa good approximation if the solenoid istightly wound and sufficiently long. Write an expression for themagnetic flux through one turn.

F = ______________

(c) What is the total flux linkage through all turns of thesolenoid? (Give your answer in terms of N, the total number ofturns, instead of n.)

NF = ______________

(d) Use the definition of self-inductance [NF = LI] to find theself-inductance of the solenoid.

L = ___________