Question

A plane of a coil of 10 turns is tightly wound around a solenoid of diameter 2 cm having 400 turns per centimeter. The relative permeability of the core is 800. Calculate the inductance of the solenoid. 

Answer 1

Given:

N = 10, d = 2 cm = 0.02 m

N = 400 turns/cm = 4 × 10⁴ turns/m

μ_r = 800

To find: Inductance of solenoid (L)   

Formulae:

1. μ = μ_rμ₀ 
2. N = nl
3. L = μn²l `((pi"d"^2)/4)`  

Calculation:

From formula (i), (ii) and (iii),

L = μ_rμ₀nN`((pi"d"^2)/4)`

= `(800 xx 4pi xx 10^-7 xx 4 xx 10^4 xx 10 xx pi xx 0.02^2)/4`

= 0.1264 H

The inductance of the solenoid is 0.1264 H.