induced current in a loop, but with symmetry plane

I'm studying the induced current in a loop of wire from AC current driven in a nearby wire. The symmetry of the fields should allow for cutting the model in half, but I'm not sure of the BC's to use on the two ends of the loop so that the induced current can flow between them. It needs a condition that says the integrated current that flows out one end equals the integrated current flowing in the other. Anyone help me with this?

Thanks.