Answer :
Answer:
The value is [tex]L = 9.164 *10^{-5} \ H[/tex]
Explanation:
From the question we are told that
The length of the solenoid is [tex]l = 30 \ cm = 0.3 \ m[/tex]
The number of turns is [tex]N = 250 \ turns[/tex]
The cross-sectional area is [tex]A = 3.5 \ cm^2 = 3.5 *10^{-4} \ m^2[/tex]
Generally the self inductance of the solenoid is
[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} \ T \cdot m/A[/tex]
So
[tex]L = \frac{ 4 \pi*0^{-7} * 250^2 * 3.5 *10^{-4} }{ 0.3 }[/tex]
=> [tex]L = 9.164 *10^{-5} \ H[/tex]