What is the Optimal Wire Spacing for a Strong Magnetic Field in a Solenoid?

[pat666]

Homework Statement

You have 12m of 0.50mm diameter copper wire and a power supply capable of passing 17A through the wire.
What magnetic field strength would you obtain inside a 2.0-mm-diameter solenoid with the wire spaced as closely as possible?

Homework Equations

The Attempt at a Solution

My problem is that I can't find n - tried about 50 times but its always wrong.
n=12/(pi*0.0205) wrong
n=12/(pi*0.02) wrong
n=0.02pi wrong never thought this was right but I can't think of anything else to do? for a mastering physics online question so no answer yet.

 

[vela]

I assume n is the number of turns per unit length.

Take a look at this picture.

http://en.wikipedia.org/wiki/File:Solenoid.svg

What limits how many turns can fit into a given length?

 

[pat666]

I thought the only limitations were the length of the wire and the radius/diametre of the solenoid?
yeah n is turns/length

 

[vela]

The turns per unit length tells you how closely you can pack the loops next to each other. The overall length of the wire and the size of the solenoid really have nothing to do with that.

 

[pat666]

really, so how do I find out n then?

 

[pat666]

hey, so n will be .0005/something

 

[vela]

Almost! You have 0.0005 m per turn, so you have 1 turn per 0.0005 m, which is 2000 turns/m.

 

[pat666]

Thanks vela! that problem had me screwed.