Physics : Self Inductance question?

Question

Suppose you wish to make a solenoid whose self inductance is 1.4mH. The inductor is to have a cross-sectional area of 1.2x10^-3 m.sq. and a length of 0.052 m. How many turns of wire needed?

Answer 1

The inductance of a solenoid is given by L = µ₀(N² / l)A. Solve for the number of turns.

N = (Ll / µ₀A)^(1/2)

= ((1.4 x 10^-3 H) x 0.052 m) / ((4π x 10^-7 Tm/A) x (1.2 x 10^-3 m²))^(1/2)

= 220 turns