Question

You need to make a 100 microH inductor on a cylinder that is 5.0 cm long and 1.0 cm in diameter. You plan to wrap four layers of wire around the cylinder.

What diameter wire should you use if the coils are tightly wound with no space between them? The wire diameter will be small enough that you don't need to consider the slight change in diameter for the outer layers.

I know that L(sol) = mu_0 N^2 A / l. I tried to put in the known numbers and solve for N but then i'm not too sure what do do with that. I don't know how to find the amount of turns in a solenoid if the give you the diameter of the solenoid and the diameter of the wire making the solenoid.

Answer 1

the number of turns: lenght/diameter of wire. Can one get them any closer than touching? In this case, since there are four layers, N=4*.05/diameter

so given N, you can calculate diameter.