Let's say my wire is like in the picture below. I understand that the $J_z$ varies depend on the cross section area.

My question: Is $J$ uniform laterally (in $xy$-plane)? enter image description here

my approach:

from Faraday's Law with time-invariant B.

$\nabla \times E = 0$

$\frac{\partial E_z}{\partial x} - \frac{\partial E_z}{\partial y} = 0$

but not clear how to proceed, especially at the boundaries.

  • $\begingroup$ a₁v₁=a₂v₂ and J=nev $\endgroup$ – Aditya Garg Feb 24 at 6:59

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