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This is a problem made by my professor.

Imagine having to repair a radio in a rural area, without any high-tech instruments, and I need to build a solenoid with an inductance of 100uH, a cross-section area of 1.00 cm2 and a lenght of 3.00cm.

Do I need to find the number of turns and their diameter, explaining also the type of material I would use?

I found some formulas, such as L = [d2 n2] / [18d + 40l] , or this L = u0 * (n2/l) * S . What's the difference between them?

https://www.electricaltechnology.org/2014/03/inductance-air-core-inductor-calculator.html (This is the link to the first formula, while the second one was found in my physics' course book).

I know that I have to find the number of turns and their diameter, the only thing I don't know is which formula do I have to use.

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    \$\begingroup\$ And you want an inductor, not a solenoid. A solenoid is an actuator, usually a type of linear motor with a coil and a moving core. \$\endgroup\$ – Transistor Apr 28 at 18:42
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    \$\begingroup\$ Try to find the equations for inductance of an air-cored inductor on a web search. Edit them into your question and do some calculations and we'll help you out. Give a guess at what would be suitable materials and where you might find them out in the country. \$\endgroup\$ – Transistor Apr 28 at 18:44
  • \$\begingroup\$ Please give us links to the places where you found these formulas, and explain what the variables are. Since this is a classwork problem we will expect you to do most of the real work and only ask a specific question if you get stuck. \$\endgroup\$ – Elliot Alderson Apr 28 at 19:44
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    \$\begingroup\$ @Transistor: in physics terminology, a "solenoid coil" is a simple coil. So "solenoid" is a valid term. Even if the word "solenoid" is usually applied to the actuator. \$\endgroup\$ – TimWescott Apr 28 at 22:51
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    \$\begingroup\$ @Tim, you're right, I'm wrong. Solenoid can refer to a simple coil. \$\endgroup\$ – Transistor Apr 28 at 22:56

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