HELP with current in loops and solenoids

[BuBbLeS01]

Homework Statement

You have a 1.1-m-long copper wire.You want to make an N-turn current loop that generates a 1.66 mT magnetic field at the center when the current is 1.01 A. You must use the entire wire. What will be the diameter of your coil?

Homework Equations

The Attempt at a Solution

I figured that this is a solenoid so I tried starting off by finding the number of turns it would take by using this equation...
LB/UI = N
The U is Mue 1.257x10^-6
I got 1438.28
but now I don't know what to do?

 

[BuBbLeS01]

does anyone know what to do for this problem?

 

[Moetasim]

Hello there,

It seems like you are on the right track in using the equation LB/UI = N to find the number of turns needed for your solenoid. To continue, you can use the formula for the magnetic field inside a solenoid, which is given by B = μ0NI/L, where μ0 is the permeability of free space, N is the number of turns, and L is the length of the solenoid.

Since you know the desired magnetic field (1.66 mT), current (1.01 A), and length of the wire (1.1 m), you can rearrange this equation to solve for the number of turns, N. Once you have the number of turns, you can use the formula for the circumference of a coil, C = 2πr, where r is the radius of the coil, to find the diameter of your coil.

I hope this helps. Good luck with your homework!