Does electrostatic induction occur if you have charged objects on both sides of a grounded conductive sphere like shown? For the sake of the purpose of this question, lets say the two charged rods have larger cross sectional areas than the sphere and that both of the rods are charged to the same potential so that there's effectively no electric field between the ends of the rods:
Can electrostatic induction occur between the rods and the sphere even if the electric field between the rods is zero? My guess would be no, because the opposing electric charge would eliminate the field lines and thus it would be as if there was no electric potential, at least as long as the sphere was within the area between the two rods:
But I suspect that there's some complication to this I'm not understanding, which is why I'm asking.