# Inductance/unit length of solenoid

1. Apr 21, 2012

### Luca13

1. The problem statement, all variables and given/known data

A solenoid is wound with a single layer of copper wire of radius 0.24 cm. The solenoid is 1 cm in diameter and 2.6 cm long. What is the inductance of the solenoid per unit length? Assume that adjacent wires touch each other and that insulation thickness is negligible.

2. Relevant equations

3. The attempt at a solution

So I am thinking that in order to find n (the number of turns of the copper wire per unit length) I need to be using the radius given for the wire. Then I can put that n in the inductance equation. The length, l, of the solenoid will cancel because the question asks for the inductance/unit length. The problem is, I keep getting this wrong and I would like to find out what I do wrong!

if r(Cu wire) = 0.0024 m --> d(Cu wire) = 0.0048
so, the number of turns per unit length = l/d(Cu wire) = 0.01/0.0048 = 2.0833

Now, L/l = (μon^2∏r(solenoid)^2l)/l = (4∏E-7*2.0833^2*∏*0.01^2) = 1.71E-9 H/m

Where is my mistake? Thank you!