Question

A piece of copper wire has a resistance per unit length of 6.45*10-3 /m. The wire is wound into a thin, flat coil of many turns that has a radius of 0.140 m. The ends of the wire are connected to a 12.0 V battery. Find the magnetic field strength at the center of the coil.

Answer 1

First calculate the resistance of the wire R, using the length L and the resistance per unit length.

You will have to leave L as an unknown. It will cancel out later.

Then calculate the current I using Ohm's law.
You will also need the number of turns of wire, N, from
N = L/(2 pi R)
For the B-field in the middle of the coil,
B = mu N I /(2 R)

Answer 2

First you have to math the answer with some formulas