Question

A 20 cm length of a long iron cored solenoid has 25 turns. If the area of cross section of the solenoid is 1 × 10⁻⁴ m², calculate its coefficient of self-inductance (L). 

Answer 1

Given: Length (l) = 20 cm

= 0.2 m

Number of turns (N) = 25

Area of cross-section (A) = 1 × 10⁻⁴ m² 

Formula: The self-inductance of a solenoid (L) = `mu_0(N^2 A)/l`

where μ₀ = 4π × 10⁻⁷ H/m

= `(4pi xx 10^-7 xx (25)^2 xx (1 xx 10^-4))/0.2`

= `(4 xx 3.1416 xx 625 xx 10^-11)/0.2`

= `(7854.0 xx 10^-11)/0.2`

= `(0.7854 xx 10^-7)/0.2`

= 3.92 × 10⁻⁷ H