# Two charged spheres connected by a wire

I have a few doubts about this problem. So we have two charged spheres of radius $$r_1$$ and $$r_2$$, one is initially charged with a charge $$Q$$, while the other one is initially without charge. The problem has a lot of questions that I already solved and I don't have any doubts about that. However, I still have one question that may be very obvious to some but I still cannot figure it out.

When the spheres are both at the same potential, they both generate an electric potential throughout space that depends on the distance to the spheres. So, if we take two separate points in the wire (and let's assume these two are really far from one of the spheres so that the electric potential of that sphere can be neglected for this particular case) there should be a potential difference between these two points because they are at different distances from the center of the closer sphere right? Then there should be current. If there's not please explain to me why. Thanks for your help whoever reads this!