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Main Question or Discussion Point
Why is the electric field just outside a conductor twice the field produced by a uniform sheet of charge?
My textbook's explanation is that you can imagine that near a point P, the charge at the surface of a conductor looks like a small uniformly charged disk centered at P, giving an electric field of magnitude σ/(2ε0) pointing away from the surface both inside and outside the surface. Inside the conductor, this field points away from point P in the opposite direction. (I understand all of this part.) It continues to say that because the net field inside the conductor is zero, the rest of the charges in the universe must produce a field of magnitude σ/(2ε0) in the outward direction. Therefore, the field cancels out the inward field produced by the disk mentioned earlier, and additionally adds on the the outward field produced by the disk to make the total field σ/(ε0). This last part is what I don't understand. Since the field produced by the rest of the charges is used to cancel out the inward field produced by the disk, how is it able to continue penetrating outward with magnitude σ/(2ε0) and add on to the outward field of the disk? Shouldn't it have already been canceled out by the disk's inward field?
I have uploaded the picture in the textbook below.
My textbook's explanation is that you can imagine that near a point P, the charge at the surface of a conductor looks like a small uniformly charged disk centered at P, giving an electric field of magnitude σ/(2ε0) pointing away from the surface both inside and outside the surface. Inside the conductor, this field points away from point P in the opposite direction. (I understand all of this part.) It continues to say that because the net field inside the conductor is zero, the rest of the charges in the universe must produce a field of magnitude σ/(2ε0) in the outward direction. Therefore, the field cancels out the inward field produced by the disk mentioned earlier, and additionally adds on the the outward field produced by the disk to make the total field σ/(ε0). This last part is what I don't understand. Since the field produced by the rest of the charges is used to cancel out the inward field produced by the disk, how is it able to continue penetrating outward with magnitude σ/(2ε0) and add on to the outward field of the disk? Shouldn't it have already been canceled out by the disk's inward field?
I have uploaded the picture in the textbook below.
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