Ampere's Law

Ampere's law states that the integral of the vector magnetic field intensity H around a closed path is equal to the total current linked by the closed path i,
int{H . dl} = sum{i}

B ---- flux density
phi -- flux
B = phi/A

H ---- magnetic field intensity
B = mu H

The magnitude of the magnetic field intensity is given by
H = i / (2 pi r)

The magnetic field intensity is unaffected by the material surrounding the conductor, but the flux density depends on the material properties, since B = mu H. Thus, the density of flux lines around the conductor would be far greater in the presense of a magnetic material than if the conductor were surrounded by air.

The product N . i is a useful quantity in electromagnetic circuits and is called the magnetomotive force, F (mmf),
F = N i A-turns