Question

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

Answer 1

Answer:

The inductance is  $L = 0.1097 \ H$

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

       $r = \frac{ 0.032 }{2} = 0.016 \ m$

The  inductance is mathematically represented as

      $L = \frac{ \mu_o * N^2 * A }{ l }$

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

             $A = \pi r^2$

=>        $A = 3.142 * (0.016)^2$

=>        $A = 0.000804 \ m^2$

 =>  $L = \frac{ 4\pi * 10^{-7} * 8400^2 * 0.000804 }{ 0.65 }$

=>    $L = 0.1097 \ H$