Question

Determine the inductance L of a 0.65-m-long air-filled solenoid 3.2 cm in diameter containing 8400 loops.

Answer 1

The inductance is
`L = 0.1097 \ H`

Step-by-step explanation:

From the question we are told that

The length is
`l = 0.65 \ m`

The diameter is
`d = 3.2 cm = 0.032 \ m`

The number of loops is
`N = 8400`

Generally the radius is evaluated as

`r = ( 0.032 )/(2) = 0.016 \ m`

The inductance is mathematically represented as

`L = ( \mu_o * N^2 * A )/( l )`

Here
`\mu_o` is the permeability of free space with value
`\mu_o = 4\pi * 10^(-7) N/A^2`

A is the cross-sectional area which is mathematically evaluated as

`A = \pi r^2`

=>
`A = 3.142 * (0.016)^2`

=>
`A = 0.000804 \ m^2`

=>
`L = ( 4\pi * 10^(-7) * 8400^2 * 0.000804 )/( 0.65 )`

=>
`L = 0.1097 \ H`