Answer:
N = 195 turns
Explanation:
The inductance of the inductor, L = 500 μH = 500 * 10⁻⁶H
The length of the tube, l = 12 cm = 0.12 m
The diameter of the tube, d = 4 cm = 0.04 m
Radius, r = 0.04/2 = 0.02 m
Area of the tube, A = πr² = 0.02²π = 0.0004π m²
[tex]\mu_{0} = 4\pi * 10^{-7}[/tex]
The inductance of a solenoid is given by:
[tex]L = \frac{\mu_{0}N^{2} A }{l}[/tex]
[tex]500 * 10^{-6} = \frac{4\pi *10^{-7} N^{2} *4\pi *10^{-4} }{0.12}\\500 * 10^{-6} = 0.00000001316N^{2} \\N^{2} = \frac{500 * 10^{-6}}{0.00000001316}\\N^{2} = 37995.44\\N = \sqrt{37995.44} \\N = 194.92 turns[/tex]
