# Current density in changing arbitrary cross section

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)?

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.

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