Making a solenoid from 1.0m of wire. missing information?

[neemer]

Homework Statement

You have a 1.0 m long copper wire. You want to make an N turn current loop that generates a 1.0 mT magnetic field at the centre when the current is 1.0 A. You must use the entire wire. What will be the diameter of your coil (in centimetres)?

Homework Equations

B = u0 * n * I

n = N/L

The Attempt at a Solution

I put in the variables and solved for n. I got 795.77. Then I know n = number of turns per unit length (N/L) but it seems that some information is missing from the question. I tried setting the unit length to 1.0m (just a random number) which gives 795.77 turns per meter. Then I know each turn uses Pi * diameter of wire. So 795.77(Pi)d = 1.0m solving for diameter i got 4.00x10^-4m or 0.04cm. But this is the wrong answer. It seems as though i would need to be given the total length of the solenoid in order to determine the required diameter.

 

[rude man]

With the given information I think you must assume the wire is very thin so you can make the "length" of the "solenoid" approach zero. In other words, the coil looks like a single loop but in actuality comprises many turns.

So, what is the expression for the B field at the center of a single-turn round coil of diameter D?

 

[neemer]

Hey thanks for the answer. so I tried using the equation

B = (u0 * N * I)/D for the magnetic field in the centre of a single coil. I set N as 1 turn and solved for D getting 0.0013m or 0.13cm. This was wrong

Then I tried this. Since the total length of the wire I need to use is 1.0m I solved for the diameter of a single loop and got 0.318m Then i used the equation and solved for N which says I would need 253.1 of these loops to make the required magnetic field. This was also wrong.

So lost on what to do next. Been going at this question for days

 

[neemer]

Ahhhh finally figured it out. Just had to get N in terms of d.

 

[rude man]

Ahhhh finally figured it out. Just had to get N in terms of d.

That's it! Congrats.