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

`2.55* 10^(-5)\ H`

Step-by-step explanation:

`\mu_0` = Permeability of free space =
`1.25664 * 10^(-6)\ N/A^2`

d = Diameter of core = 12 mm

r = Radius =
`(d)/(2)=(12)/(2)=6\ mm`

l = Length of core = 8.4 cm

N = Number of turns = 123

Inductance is given by

`L=(\mu_0N^2\pi r^2)/(l)\\\Rightarrow L=(1.25664 * 10^(-6)* 123^2* \pi * 0.006^2)/(0.084)\\\Rightarrow L=2.55* 10^(-5)\ H`

The self-inductance of the solenoid is
`2.55* 10^(-5)\ H`