In this sort of 2D formulation, everything acts as if it is "shorted together at infinity" unless you specifically impose a connectivity on things via "circuit" properties. You need to define another "circuit" that carries a total current of zero and apply this property to your conductive core region to make the core region to behave as if it unterminated.This is impossible?! The core material is finite in length and unterminated. The current has no place to flow, therefore cannot exist. Is this assumption correct?