Potential of a conductor in a non-uniform E field

imagine there is a positive pt charge somewhere in space. so the E field due to this pt charge, falls off with distance.


now, i place a conducting rod parallel to the field some distance away,
such that one end of the rod is at V_A and another end is V_B
(where V_A > V_B)

we also know that there can be no net E-field in a conductor. so potential must be constant throughout a conductor.

my question is. what is the potential?? V_A or V_B? or what?