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

## 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)?

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.

## The Attempt at a Solution

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rude man
Homework Helper
Gold Member
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?

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 feild. This was also wrong.

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

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

rude man
Homework Helper
Gold Member
Ahhhh finally figured it out. Just had to get N in terms of d.
That's it! Congrats.