A tightly wound solenoid of 1600 turns, cross-sectional area of 6.00 cm2, and length of 20.0 cm carries a current of 2.80 A. (a) What is its inductance? (b) If the cross-sectional area is doubled, does anything happen to the value of the inductance? Explain your answer.

(a) 9.65 mH

(b) doubled

Explanation:

A = 6 cm^2 = 6 x 10^-4 m^2, l = 20 cm = 0.2 m, i = 2.8 A, N = 1600

(a) The formula for the self inductance of a solenoid is given by

L = μ0 N^2 A / l

L = 4 x 3.14 x 10^-7 x 1600 x 1600 x 6 x 10^-4 / 0.2

L = 9.65 x 10^-3 H

L = 9.65 mH

(b) As we observe that the inductance is proportional to the area so if the area is doubled, then inductance is also doubled.