How Does Coil Dimension Affect Magnetic Field Strength?

[gamesandmore]

A piece of copper wire has a resistance per unit length of 6.40e-3 ohm/m. The wire is wound into a thin, flat coil of many turns that has a radius of 0.190 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.

R/L = 6.40e-3 ohm/m
r = 0.190 m
V = 12.0 V
u0 = 4pi e -7 Tm/A
B = ? T

Equations:
V = IR (I = V/R)
B = u0 * n * I
so B = u0 * n * (V/R)

I don't know where to go from here.

 

[Dick]

Start by finding L in terms of n. That may be your missing ingredient.

 

[gamesandmore]

n = turns/L
L = R/6.40e-3 ?
im lost here

 

[learningphysics]

Did you post the question exactly?

What I'm thinking is... can't you arbitrarily make the coil longer, keeping the number of turns/unit length the same... but increasing the resistance... thereby lowering the current. And that would lower the magnetic field?

So is there a unique solution to this problem?