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In the Classic Image problem we take a charge $+Q$ and place at a distance $d$ above an infinite conducting plate.

Now the conducting plate is grounded (at a potential zero ). The charge $+Q$ induces $-Q$ charge on the conductor. Now the charge $+Q$ (produced because of separation of charge $-Q$) is a free charge, it's gets grounded, so after induction and grounding we have $-Q$ on the conducting surface held by $+Q$ at a distance $d$. Now my question is now that the conducting plate has some charge $-Q$ on it, won't the conducting plate have a non zero potential?

Classic Image problem Classic Image Problem

How does the problem remain unaffected when we replace the conducting plate by an equal and opposite negative charge at a distance $-a$?

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  • $\begingroup$ Why do you write like this? "something .Something more ,even more ." it should be "something. Something more, even more." Punctuation then space and not space then punctuation. See post before edit. $\endgroup$
    – Mauricio
    Commented Sep 6, 2022 at 11:30

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The presence of a net charge on a conductor does not necessarily mean that conductor has zero potential.

Here is another example to get you used to this idea. Consider an ordinary circuit with a capacitor $C$ and a voltage source (battery) $V$. Connect one part of the circuit to ground. Now you have zero potential on one side of the capacitor, but the charge on that side is still either $V C$ or $-V C$.

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