Hi everyone, I have a question (or three) regarding Purcell's discussion of image charges, in pg 137-139 of the third edition of his EM book. He goes over the classic image charge example: a plane held at zero potential, and a charge [itex] Q [/itex] a distance [itex] h [/itex] above it. I'm fine with everything he says, up until the following: "returning to the actual setup with the conducting plane, we know that in terms of the surface charge density [itex] \sigma [/itex], the electric field just above the plane is [itex] E_z = \sigma / \epsilon_0 [/itex]." My problem with this is that he then proceeds to plug in the expression for [itex] E_z [/itex] that he had determined from the image charges situation. But this [itex] E_z [/itex] corresponds to the electric field due to the whole system, charge [itex] Q [/itex] included. So why would [itex] E_z [/itex] correspond to just the contribution from the plane, [itex] \sigma / \epsilon_0 [/itex]? That's my first question. My second question stems from the following; having found the charge distribution on the plane, he integrates through the whole plane to find that the total charge on it is [itex] -Q [/itex], and explains that even if the plane initially had zero charge, this makes sense. The justification he gives is that a compensating positive charge [itex] Q [/itex] is spread over the whole plane, but that its contribution to the electric field [itex] E_z [/itex] is negligible (since the charge density will be zero in the infinite plane). I have the following problem with this argument: It seems like the charge distribution [itex] \sigma [/itex] should somehow be balanced by the positive charge, so that it integrates to zero at infinity. Otherwise, it's not the actual (real, physical) charge distribution! (Since the plane had zero charge to begin with.) It's just the approximate distribution that we find at points near the origin of the plane (below the charge [itex] Q [/itex].) Then I have an extra bonus question :) Purcell argues that the field below the plane must be zero, because "we can consider the conducting plane to be the top of a very large conducting sphere, and we know that the field inside a conductor is zero." But I have a huge problem with this. If we consider the plane to be that (the top of a sphere), then we have different boundary conditions from before! So it becomes a little sketchy, in my opinion, to use this argument, and combine it with the image charges he used (which definitely don't satisfy the boundary conditions of zero potential along the whole "big sphere" that Purcell is imagining; it just had zero potential along the infinite plane). How is this justified? Can anybody give another argument why the field below the plane must be zero? As you can probably tell, I had a lot of trouble following this discussion. Any help would be appreciated!