Answer:
The inductance is [tex]L = 0.1097 \ H[/tex]
Explanation:
From the question we are told that
The length is [tex]l = 0.65 \ m[/tex]
The diameter is [tex]d = 3.2 cm = 0.032 \ m[/tex]
The number of loops is [tex]N = 8400[/tex]
Generally the radius is evaluated as
[tex]r = \frac{ 0.032 }{2} = 0.016 \ m[/tex]
The inductance is mathematically represented as
[tex]L = \frac{ \mu_o * N^2 * A }{ l }[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with value [tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]
A is the cross-sectional area which is mathematically evaluated as
[tex]A = \pi r^2[/tex]
=> [tex]A = 3.142 * (0.016)^2[/tex]
=> [tex]A = 0.000804 \ m^2[/tex]
=> [tex]L = \frac{ 4\pi * 10^{-7} * 8400^2 * 0.000804 }{ 0.65 }[/tex]
=> [tex]L = 0.1097 \ H[/tex]
