Question

Can there be a potential difference between two adjacent conductors carrying the same charge?

Answer 1

Yes, if the sizes are different.

Explanation: We define capacitance of a conductor C = Q/V is the charge of conductor and V is the potential of the conductor. For given charge potential V `oo` 1/C. The capacity of conductor depends on its geometry, so two adjacent conductors carrying the same charge of different dimensions may have different potentials.