Why there is a distance dependence in coulombs law if photons can travel to infinity? Why there is distance dependence at all?
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Qmechanic
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It is not clear why you think the distance dependence in Coulomb's law should have something to do with the maximum distance photons can travel. Coulomb's law is first and foremost a purely classical result of electromagnetism, where there are no photons. For its quantum derivation, see https://physics.stackexchange.com/q/142159/50583. – ACuriousMind Jul 28 '18 at 09:00
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@ACuriousMind, okay why force, provided by classic electric field decreases with distance? – Jul 28 '18 at 09:03
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The simplified explanation is that photons spread out as they get further away from the source. And the strength of the electromagnetic force is roughly related to number of photons per unit cross-sectional area, not just the number of photons itself. So as the photons spread out and the area grows (as $r^2$), the strength of the force drops (as $1/r^2$).
For more details on the connection between photons and the electromagnetic force, you might want to see this question and others like it.
David Z
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I know about the photoelectric effect, and according to it You are absolutely wrong. The intensity (number of photons) doesn't influence on the force, the frequency (and hence the energy) of single photon does it – Jul 28 '18 at 09:39
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Plus, You wrote "photons spread out as they get further away from the source". How it deals with the fact that energy can be radiated only by simplest part? I mean, can an electron emits 2 or more photons per time? – Jul 28 '18 at 09:43
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@Artur, the frequency determines the energy quantum, and number of photons determine how many energy quanta you deliver. So of course intensity has influence on the force. – wcc Jul 28 '18 at 09:44
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@IamAStudent https://en.wikipedia.org/wiki/Photoelectric_effect ctrl f "It explained why the energy of photoelectrons was dependent only on the frequency of the incident light and not on its intensity" – Jul 28 '18 at 09:50
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@Artur, exactly. The measured energy quantum was a function of frequency, not intensity. Now if you scatter multiple energy quanta per second you get force, and the more you scatter the stronger the force is. Search radiation pressure / scattering force / laser cooling – wcc Jul 28 '18 at 09:56
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@IamAStudent, so, according to this, and the fact, that energy can be absorbed only by quant per time, there should not be a dependence of how much photon will be meet, and hence the distance between particles. No? – Jul 28 '18 at 10:01
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@Chair first time hearing it. I confused I didn't understood anything yet.. If I have electron with energy 3 and two photons with energy 5, as I understand, when electron absorb one photon its energy become 5, not 8, and then if it absorb the second one it will be again 5, why I wrong? – Jul 28 '18 at 10:30
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@Artur I don't imagine multiphoton stuff are directly relevant to your main question about intensity and distance... I just wanted to point out that they're something to keep in mind. The point is, informally put, if you have a huge number of low-energy photons, there's a chance that an atom will be ionised by absorbing multiple photons. But if you have a small number of incident photons, odds are the atom will absorb a low energy photon and then release it before it absorbs enough photons to get ionised. That description leaves out of stuff, but it serves the purpose here. – Jul 28 '18 at 10:39
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