You have a 1.8m long copper wire. You want to make an N-turn current loop that generates a 2.0mT magnetic field at the center when the current is 1.3A . You must use the entire wire.. What will be the diameter of your coil?

The diameter is  0.022m.

Explanation:

The magnetic field at the center of the coil is given by

(1).

where is the magnetic constant, is the current, number of coils, and is the diameter of the coil.

Now, if we call the length of the wire, then it must be true that

(this says coil circumferences () fit into )

putting this into equation (1) we get:

solve for

putting in the numerical values

we get:

this would be about 43%