Quote by adityatandon
Consider the classic image problem with a conducting plane and a point charge. After finding out the charge density on the plane we integrate to find out the total charge induced. It comes out to be "q",where q is the charge outside
My book says "It comes out to be q, as you can convince yourself with the benefit of hindsight". It isn't that obvious why it should come out equal to the image charge. Can somebody explain?

At distant points the field due to the charge and its image cancel each other out. Now, since in fact the image is not there and the field is indeed caused by the induced charge, the sum of the induced charge and the point charge must be zero otherwise the field at distant points wouldn't be zero.