Question

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be ______.

पर्याय

• 2592

• 2866

• 2976

• 3140

Answer 1

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be 2866.

Explanation:

Given: Inductance (L) = 0.016 H

Length of solenoid (l) = 0.81 m

Radius of solenoid (r) = 0.02 m

Permeability of free space (μ₀) = 4π × 10⁻⁷ T ⋅ m/A

N = number of turns

Area of cross-section (A) = πr²

= π(0.02)²

= 4π × 10⁻⁴ m²

To determine the number of turns in the solenoid, we can use the formula for the inductance L of a solenoid:

L = `(mu_0N^2A)/l`

0.016 = `(4 pi xx 10^-7 xx N^2 xx 4pi xx 10^-4)/0.81`

Simply to solve for N²:

N² = `(0.016 xx 0.81)/(4 pi xx 10^-7 xx 4 pi xx 10^-4)`

= `0.01296/(16 pi^2 xx 10^-11)`

= `0.01296/(1.57896 xx 10^-9)`

N² ≈ 8219479.5

N = `sqrt 8219479.5`

N = 2866

Thus, the number of turns in the solenoid is approximately 2866.