Why boundary condition in steady electric current?

[mai fouad]

when we electric field between two conductors in certain direction the current density should pass in its direction why current density direction change at boundary although the direction of electric field is the same for both conductors

 

[Simon Bridge]

The current density does depend on the electric field strength, but it does not depend only on the electric field strength.

The diagram shows two materials with different conductivities in parallel - if they have the same cross-section, the currents will depend on their conductivities right? That's just the parallel resistors rule.