Magnetic field = 0 inside a conducting wire?

[Nikitin]

Hey. If a wire is conducting electricity and all the current is concentrated at the edge of the wire, as in the skin effect, the magnetic field everywhere inside should be zero due to symmetry when applying biot-savarts law.

However, according to ampere's law, it shouldn't. I take a cross-section of the wire and apply an annulus surface where the the outer ring covers the current I penetrating the cross-section, while the inner ring defines the integral ∫B*dl. The radius of the inner ring is r.

Then ∫B*dl = Iμ => B = Iμ/2pi*r

How is this contradiction possible? Am I applying ampere's law wrong?

 

[mfb]

You cannot use different (arbitrary) rings/surfaces to calculate current and magnetic field. You can choose an area with current inside - but then the edge of this area will be outside, too. Or you can choose an area where the edge is inside - but then you do not have a current flowing through.