Let's use Ampere's Law to find the field inside a long straight wire of radius R carrying a current I. Assume the wire has a uniform current per unit area:
J = I/pR2
To find the magnetic field at a radius r inside the wire, draw a circular loop of radius r. The magnetic field should still go in circular loops, just as it does outside the wire.
Apply Ampere's Law:
ò B · ds = 2prB = mo Ienc
The current passing through our loop is the current per unit area multiplied by the area of the loop:
Ienc = Js pr2 = Ir2/R2
Therefore 2prB = mo Ir2/R2
B = moIr/2pR2
So, inside the wire the magnetic field is proportional to r, while outside it's proportional to 1/r.