As a high school student studying electrostatics, I understand that the electric potential at a point closer to a charged particle, is nearly infinite, then why there exist a finite potential difference between two charged objects that are in contact with each other? For example between an electrolyte and its electrodes that are kept close to each other in an electrolytic cell.
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$\begingroup$ Why is a strange that a potential difference can be either finite or infinite, depending on the situation? Distance can be finite or infinite. $\endgroup$– GhosterCommented Mar 4 at 18:15
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$\begingroup$ Does this help? physics.stackexchange.com/q/784247/334569 $\endgroup$– Stevan V. SabanCommented Mar 5 at 2:04
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$\begingroup$ And physics.stackexchange.com/a/747129/334569 $\endgroup$– Stevan V. SabanCommented Mar 5 at 16:49
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I understand that the electric potential at a point closer to a charged particle, is nearly infinite
This is not true in general, but is specific to a classical point charge. Many other configurations of charge density besides a classical point particle do not have this behavior.
why there exist a finite potential difference between two charged objects that are in contact with each other?
Because the charge distribution is not approximately a classical point particle. On large scales the distribution is a surface polarization density rather than a point charge. On microscopic scales the charges are quantum mechanical rather than classical, and quantum mechanics keeps them separated enough for the forces and potentials to be finite.
