Can there be a potential difference between two adjacent conductors carrying the same charge
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Yes.The one which is having the smaller charge will have the greater potential.
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Answer:
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 ∝ 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.
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