Charge on a grounded conductor w/ method of images

AI Thread Summary
The discussion centers on the method of images used to determine the induced charge on a grounded conductor near a point charge. It highlights that the total charge, as derived from Gauss's law, is equivalent to the image charge. The link provided directs to a Wikipedia article that explains this concept further. The key point is that both the actual surface charge and the image charge produce the same electric field, leading to this equivalence. Understanding this relationship is crucial for applying the method of images effectively.
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Why is it that whenever the method of images is used to solve for the induced charge on a grounded conductor in the presence of a point charge, the total charge is just the same as the image charge?
 
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Gauss's law says that \oint{\bf E\cdot dA} is given by the total charge inside.
This is either the actual surface charge or the image charge, since they give the same E.
 
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