# acquiring conductivity through curl of magnetic field density and Ampere's circuital law

I have some question.

I want to acquire conductivity and I used Ampere's circuital law.

The problem is

A solid conductor of circular cross section with a radius of 5mm has a conductivity that varies with radius. The conductor is 20m long and there is a potential difference of 0.1V DC between its two ends. Within the conductor, H = 10^5 * p^2 (A/m)

But the solution(I'm solving Engineering Electromagnetics 8th edition W.Hayt) solved that problem through curl of magnetic field. To be specific, it gets current density(J) from curl of magnetic field density and put it in to

'conductivity = J / E(electric field)'

Yes I understand that is solution. But my question is that can't I use Ampere's circuital law. I solved like this.

2pi * p * H = pi * p^2 * conductivity * E

Right hand side term of yours $2\pi\,p\,H=\pi p^2 \sigma E$ is wrong because it implies conductivity to be constant over the whole section up to p radius.
It could be turned into an ODE like $2\pi\,p\,H=\int_0^p 2\pi r\,\sigma(r) E \,\mathrm{d}r$ to be solved for $\sigma(r)$ though