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Two conducting planes meeting at a right angle with a point charge q located at (x, y, z) = (a, 0, a) .

The conducting planes are located on the x and z axis.

My answer was one negative charge at (-a, 0, a) and another negative charge at (a, 0, -a). That way the potential at the x and z axis will be 0.

The answer book states that a positive charge at (-a, 0, -a) is needed, because '' One can visualise that the mirror charges at (a, 0, −a) and (−a, 0, a) would induce (positive) surface charges on the conducting planes located at (0, 0, z) and (x, 0, 0), respectively ''.

I have a hard time picturing why this would mean that there is a positive surface charge on the conducting planes, and why does a third image charge solve this?

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  • $\begingroup$ The conducting planes are located on the x and z axis. What does this mean? Planes are not located on axes. $\endgroup$
    – G. Smith
    Commented Mar 10, 2020 at 20:11
  • $\begingroup$ With two negative image charges, are the two conducting planes equipotential surfaces? $\endgroup$
    – G. Smith
    Commented Mar 10, 2020 at 20:13
  • $\begingroup$ Note that you are not putting the negative charges one by one but all at once.The charge at (-a,0,a) makes the "z axis plane" equipotential but dont forget that the (a,0,-a) is also present there and disrupts the equipotentiality of the "z plane".Similarly the effect of charge (a,0,-a) to make the "x axis plane" an equipotential surface,cannot be achieved due to presence of the 1st image charge at (-a,0,a)! To balance this effect we need to introduce a third positive charge placed symmetrically at (-a,0,-a). $\endgroup$
    – Manas Dogra
    Commented Mar 11, 2020 at 15:47
  • $\begingroup$ Also,as pointed out by G. Smith-- planes are not located on axes,which is why i called gave quotes in "x axis plane" and "z axis plane" in the previous comment. As this is a very well known problem,what you clearly meant is,what can be called Y-Z plane and X-Y plane. $\endgroup$
    – Manas Dogra
    Commented Mar 11, 2020 at 15:51

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