Ressistance when current-density is not constant

[center o bass]

I am trying to figure out how it would effect the ressistance R of a wire with length L and variyng cross-sectional area A(x) if the current density was a fuction of the radius of the wire. That is J = J(r).

I'm having trouble with this when it seems like ressistance is the result of a derivation of ohm's law assuming constant E-field such that $$E = \frac{J}{\sigma} = \frac{V}{l}$$, but if E is not constant how can one then relate the ressitance to the current-density J?

A qualitative answer is good enough.

 

[aim1732]

But if E is not constant how can one then relate the resistance to the current-density J?

Resistance is by definition ΔV/i(and this is not Ohm's Law).Even though the electric field is not constant it is a law accurate for differential elements. So if you calculate E(x) function and integrate for the corresponding potential drop you can calculate resistance.