Solenoid and iductance help?

Question

A solenoid has N turns of area A distributed uniformly along its length, script i. When the current in this solenoid increases at the rate of 3.3 A/s an induced emf of 51 mV is observed.

(a) What is the inductance of this solenoid?

(b) Suppose the spacing between coils is doubled. The result is a solenoid that is twice as long but with the same area and number of turns. Will the induced emf in this new solenoid be greater than, less than, or equal to 51 mV when the current changes at the rate of 3.3 A/s?

(c) Calculate the induced emf for part (b).

Answer 1

A. V = Ldi/dt ==> L = V/(di/dt) = 0.01545 H

B, C. L is proportional to N^2*area/length; twice the length  = half the inductance, half the voltage.