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This is a doubt on the method of images from J.D Jackson's Classical Electrodynamics first edition, Chapter 2. While trying to find the potential of the configuration of a conducting sphere and charge, he says that by symmetry, the image charge $q'$ must lie on the ray joining the center of the sphere and charge $q$, where $q$ is the original charge and $q'$ the image charge. Mathematically, one can show it by using Apollonius' circles, but what is the symmetry that the author is talking about, which ensures that the charges and centre of sphere must be collinear?

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The set up is symmetric above and below the axis containing the sphere centre and charge, so the solution must also be symmetric about this axis. If we want the simplest solution of one image charge, it must lie on this axis.

More precisely, you could say there is azimuthal symmetry present (the solution should look the same if I rotate the system about the special axis).

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  • $\begingroup$ Also, mirror symmetry. $\endgroup$ Jun 16, 2023 at 12:10
  • $\begingroup$ So can we have solutions where the charge doesn't lie on the axis? Also, we are emphasizing azimuthal symmetry here because the thing we are looking for(the potential) is a scalar quantity right? $\endgroup$
    – V Govind
    Jun 16, 2023 at 13:40

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