I have asked this question before on various fora, but I never got a really satisfactory answer. Perhaps physicists simply don't know... Anyway I'm asking again; an electric field emanating from, say a small pointed metal electrode, is for many practical purposes a continuous field that is "infinitely differentiable". To me this means that if you are at a distance of e.g. 3 cm from the electrode and then move 10 Å further from the electrode the field strength will diminish exactly in proportion to the extra distance. However I have an intuitive feeling that this is not really true; that there are really "steps" in the field. You move 5 Å and nothing happens to the field strength and then at 12 Å the field changes abruptly by an integer multiple of something. So am I right or wrong? What are you comments? Is my intuition correct about quantization of fields? Is it possible to put numbers on this? Include Planck's constant in some formula? S.A.