Question

You need to produce a solenoid that has an inductance of 2.51 μH . You construct the solenoid by uniformly winding 1.17 m of thin wire around a tube. How long, in centimeters, should the tube be?

Answer 1

L=2.51•10⁻⁶ H
x=1.17 m
z=?
L=μ₀N²A/z
N=x/2πr => r= x/2πN =>
A=πr²=πx²/4π²N²
L=μ₀N²A/z= μ₀N²πx²/4π²N²z=
= μ₀x²/4z
z= μ₀x²/4L= 4π•10⁻⁷/4•2.51•10⁻⁶=0.12 m

Answer 2

Thanks Elena. I was really stuck on the N=x/2πr. I didn't know that was a property.

But I believe there is an error in the math

z should be z= μ₀x²/4πL = .054 m

Thanks again