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I have an electric dipole that is located at a distance $a$ from two infinite conducting planes that form a right angle between them.

I'm asked to find the electric potential in all the points that are on a line that passes through the vertex of the conductor and the dipole (i.e. a line that forms an angle of $45º$ with the horizontal) and the induced charge in the conductor.

I thought of doing this with the method of image charges, where 4 dipoles would result. But the conductor is not grounded (at least, that is not specified), so: can this method be used? Both if the answer is "yes" or "no": why? If it is not grounded, couldn't I assume that I will take my potential reference as the conductor and that would "ground it"? I'm confused with this: I don't know if "grounding" something just means that the potential reference will be there or if it implies something else I'm ignoring.

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2 Answers 2

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Anytime you hear infinite conducting plates, the plates are at $0$ potential. Why? Because, the plates extend till infinity, where the potential is conventionally $0$, and since conductors are equipotentials, the entire plate is at $0$V.

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  • $\begingroup$ This is not true in general. If you have an infinte comducting plate in the x-y plane, which infinity according to you has potential zero? At z= infinity or at x/y = infinity? ,conventionally, labelling any one zero will make the other non zero. $\endgroup$
    – Lelouch
    Sep 22, 2016 at 12:46
  • $\begingroup$ @Lelouch Like the Earth the conducting plates are assumed to have infinite capacitance. Therefore however much the charge on them is redistributed they remain at zero potential. $\endgroup$ Sep 24, 2018 at 21:35
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Even if the plates aren't at $0$ you can apply the method of images, assuming they're at zero. Then, as the last step, just add the potential the plates are to to the potential you found in step one to get the answer.

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