Physics
posted by Mary on .
A piece of copper wire has a resistance per unit length of 5.95 103 /m. The wire is wound into a thin, flat coil of many turns that has a radius of 0.200 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.
In this question do I use the following formula:
F = /q0/v(permeability of free space x I / 2piR) sin theta

The field at the center is proportional to the number of turns, N, but the current is inversely proportional to then number of turns (because increasing N increases the resistance). Therefore N cancels out.
B = mu*N I /(2r)
(For a reference to that formula, see (Broken Link Removed)
r is the loop radius; R is the total resistance of all N turns
I = V/R
R = (resistance per length)* 2 N pi r
I = V/((resistance per length)* 2 N pi r)
B = mu*V/((resistance per length)* 4 pi r^2)