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/πR²

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:

∫ B • ds = 2πrB = μ_o I_enc

The current passing through our loop is the current per unit area multiplied by the area of the loop:

I_enc = J_s πr² = Ir²/R²

Therefore 2πrB = μ_o Ir²/R²

B = μ_oIr/2πR²

So, inside the wire the magnetic field is proportional to r, while outside it's proportional to 1/r.