Question

A solenoid has 123 turns of wire uniformly wrapped around an air-filled core, which has a diameter of 12 mm and a length of 8.4 cm. The permeability of free space is 1.25664 × 10−6 N/A 2 . Calculate the self-inductance of the solenoid. Answer in units of H

Answer 1

Answer:

$2.55\times 10^{-5}\ H$

Explanation:

$\mu_0$ = Permeability of free space = $1.25664 \times 10^{-6}\ N/A^2$

d = Diameter of core = 12 mm

r = Radius = $\frac{d}{2}=\frac{12}{2}=6\ mm$

l = Length of core = 8.4 cm

N = Number of turns = 123

Inductance is given by

$L=\frac{\mu_0N^2\pi r^2}{l}\\\Rightarrow L=\frac{1.25664 \times 10^{-6}\times 123^2\times \pi \times 0.006^2}{0.084}\\\Rightarrow L=2.55\times 10^{-5}\ H$

The self-inductance of the solenoid is $2.55\times 10^{-5}\ H$