A month back I began my course in classical electrodynamics. I know about the field lines of moving charges. But I have this question that if an electron and a positron are situated some distance apart and assuming that the electric force is 'somehow' great enough to accelerate them towards each other, then what happens to the electric field lines after the 2 have collided? The net charge becomes 0 and taking into the fact that photons are released, my question is what happens to the electric field?   Edit - So is it that the Electric Field exists outside the radius ct and is zero within the circle of radius ct which increases in diameter with time and spreads in space ?
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Short Setup  I am curious about the the mechanics of fields, whether , , etc.  So as a specific example in order to simplify (hopefully) how to ask this question, consider  or , specifically interactions between .  My specific curiosity is in how we handle the "sudden" creation or loss of a source and how the source then creates its associated field.  My naive guess is that the loss of a source (e.g., annihilation) might be easier to handle, but let's focus on creation of a source for now.  Questions  The specific example of pair production interested me because I was wondering:   How does the field arise from the sources?   Meaning, is it delayed until after the source  fully "condenses" from the , for instance? Or does the field slowly "turn on" as the source "condenses"?   Perhaps I should have asked whether it we know if it takes time for sources to form (I assume it does).  If so, can we describe this from first principles or is it empirically based?  Am I asking that in a very uncomfortable manner?  If so, I would appreciate any suggestions.  For instance, is there a better word than "condense"?  I was thinking about water condensation as a very loose analogy to the purpose of the Higgs field in the formation of massive objects.  Why can they be produced without immediately recombining?   That is, how "close" are the two sources spatially after formation and what energies are needed to overcome the associated potential?  Does the field emanate/propagate as if from a point source?   I ask because I am trying to determine whether this is a simple  issue (i.e., far away it's just like a point source) or if the field emanates only from the "surface" of the source (e.g., ). If it starts from "within" the source as the source forms, do we know how to handle this mathematically?   My concern arises from the "similar" problem of bubble formation, where the bubble starts with zero radius which would require an infinite energy.  Perhaps the analogy is not appropriate?     Purpose  I ask these questions because it struck me this morning, while driving to work, that I did not know how and when a field "turned on."  I started to think about pair production and then quickly became confused (not difficult to do) and thought many of the quantum whisperers on this site would be much better at explaining these nuances than any of my failed rummaging through Wikipedia or scholarly articles and old text books.
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As written in Principles of Physics by Halliday, Resnick and Walker:     The electric field is a vector field; it consists of a distribution of vectors,one for each point in the region around a charged object. In principle, we can define the electric field at some point near the charged object. We first place a positive charge $q_0$, called a test charge,at the point. We then measure electrostatic force $\vec{F}$ that acts on the test charge. Finally, we define the electric field $\vec{E}$ at that point due to the charged object as $$\vec{E} = \frac{\vec{F}}{q_0}$$ .   So, this is the way they derive the electric field. But one thing that perplexes me is that as test charge has its own field, so when the test charge is introduced in the field of concerned charged object, say another point charge $+q$ , won't it get shifted due to the repulsion from the test charge $q_0$ (which is, by convention, positive)? Then consequently the field of $+q$ will also be shifted. In a word, it will get disturbed by that test charge. But the book derived the formula as if the positive point charge $+q$ remained fixed i.e. the test charge had no effect on the field of the point charge. But how can it be? If the test charge $q_0$ is a charge, then obviously it has also field which will exert force on $+q$. So how can the formula be true? Why did the book neglect this?  This phenomenon can be compared to earth's gravitational field. When a body moves upward, it exerts force on the earth downward. But as the earth has huge mass, its shifting can be neglected and hence it doesn't affect its gravitational field.   But here it is a point positive charge; it has no huge mass. So why did the book neglect its shifting and how can the formula be true? Please help.
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Frequently when EM waves are taught, it is said that the change in electric field causes a change in the magnetic field, which then causes a change in the electric field, and so on and so forth.   But from my understanding of basic electromagnetics, it is not necessarily a changing electric field that creates a change in magnetic field, but instead an accelerating charge. and it is this charge that creates both the electric and magnetic field. Again, from my understanding, a changing magnetic field is not generated by a changing electric field, but instead just happens to always be present perpendicular to a changing electric field due to the laws of electromagnetism.   Am I wrong? Or is the "mutual generation" concept between the electric and magnetic components of an EM wave an actual thing?
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My physics textbook says "Electrostatic field lines do not form closed loops. This is a consequence of the conservative nature of electric field." But I can't quite understand this. Can anyone elaborate?
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Can a free electron with a constant velocity V то move eternally at this rate in the inertial frame? The question arises from the fact that a moving charge creates near its trajectory varying electric and magnetic fields. Whether kinetic energy of electron is spent for it?
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According to classical electromagnetic theory, accelerated charges should emit radiation and lose energy.  The reason given in my book why atoms don't emit radiation (say, when the atom moves along a circle) is because the atom is neutral. I can understand how this works for a neutral particle like a neutron but the atom has constituent charges within in. How can the "presence" of an opposite charge nearby stop what seems to be an intrinsic process independent of the surroundings? Do the electrons and protons emit radiation that destructively interferes or something of that sort?
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Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function spreads out, and there is a small but finite chance of finding it pretty much anywhere in the universe. Suppose it's measured one second later by a different observer more than one light second away and, although extremely unlikely, this observer discovers that electron. I.e. the electron appears to have traversed the intervening distance faster than light speed. What's going on here?  I can think of several, not necessarily contradictory, possibilities:   I'm misremembering how wave functions work, and in particular the wave function has zero (not just very small) amplitude beyond the light speed cone. Since we can't control this travel, no information is transmitted and therefore special relativity is preserved (similar to how non-local correlations from EPR type experiments don't transmit information) Although the difference between positions is greater than could have been traversed by the electron traveling at c, had we measured the momentum instead, we would have always found it to be less than $m_e c$ and it's really the instantaneous momentum that special relativity restricts; not the distance divided by time. My question is ill-posed, and somehow meaningless.   Would anyone care to explain how this issue is resolved?
117021
I have recently been reading about Quantum Electrodynamics which I found very interesting, but even more confusing.  I understand photons mediate the electromagnetic force and interactions between charges can be described by virtual photon exchange. And that in Quantum Mechanics particles paths can be evaluated by sum over all paths...  An electron travelling from one point to another will take all paths, emitting and reabsorbing virtual photons. Does the electrons take all paths including those that involve faster than light velocities?  Is this question null, Does it mean anything to ask about properties of virtual particles?  Do I have the wrong idea about what virtual particles are?
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According to QFT, virtual electron-positron pairs are created everywhere in the space, and more frequently near electric charges. Suppose that one such a pair is created in the proximity of an electron. Is it possible for the initial electron to annihilate with the created positron, leaving behind the created electron?  If so, the position of the created electron would not be the same as the initial electron, so this effect would change the position of the electron we observe in that region of the space, creating some kind of uncertainty in position. Is there any quantitative measure of such an uncertainty in position due to vacuum fluctuations?
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In case of a charged particle which is travelling at a uniform velocity, the electric field due to it at a given point doesn't change instantaneously . The reason for this delay in change of electric field , physically , can be explained as the time the electric field needs to propagate to that point, or, let's say, the change in electric field takes some time to propagate .  I would like to know what exactly does it mean by a propagating electric field, and how exactly does it propagate  ? What can we put forth as a reason to explain this propagation at a speed equal to the speed of EM radiations ? (I hope the coming up answers would comprise an important part explaining this physically. ) I guess we can derive the speed of EM radiation from Maxwell's equation ; can we show that this propagation too has the same speed ?
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I know this isn't the right place for asking this question, but in other places the answers are so awfull.. I'm studying eletricity, so, I start seeing things like "charges", "electrons has negative charges",etc. But I didn't quite understand what charge is. I search a little bit on the internet and found it related to electromagnetic fields, then I thought "negative and positive may be associeted with the behaviour of the particle in the field, great!", but the articles about e.m. fields already presuppose "negative" and "positive" charges. In other places, I see answers relating charges to the amount of electrons/protons in an atom, but if that's right, the "negative" electron is an atom without any protons? What about the neutron? So, my questions are (1) What are charges; and (2) How a particle can "be" electrically charged. What does that really mean? Thanks for your time.
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Pardon me for my stubborn classical/semiclassical brain. But I bet I am not the only one finding such description confusing.  If EM force is caused by the exchange of photons, does that mean only when there are photons exchanged shall there be a force? To my knowledge, once charged particles are placed, the electromagnetic force is always there, uninterruptedly. According to such logic, there has to be a stream of infinite photons to build EM force, and there has to be no interval between one "exchange event" to another. A free light source from an EM field? The scenario is really hard to imagine.  For nuclei the scenario becomes even odder. The strong interaction between protons is caused by the exchange of massive pions. It sounds like the protons toss a stream of balls to one another to build an attractive force - and the balls should come from nothing.  Please correct me if I am wrong: the excitations of photons and pions all come from nothing. So there should be EM force and strong force everywhere, no matter what type of particles out there. Say, even electrical neutral, dipole-free particles can build EM force in-between. And I find no reason such exchanges of particles cannot happen in vacuum.   Hope there will be some decent firmware to refresh my classical brain with newer field language codes.
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Since electromagnetic waves have both electric and magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation. How much is that electric charge? Can you possibly get a shock in some way?
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Imagine a negatively charged conductor in a vacuum. The excess electrons will be spread out over the surface such that the net electric field inside the conductor is zero.  What keeps these extra electrons bound to the conductor?   For the case of a neutral conductor, I could intuitively understand some sort of Coulomb force being responsible. But for a negatively charged conductor, I don't understand what (net?) positive entity is exerting the attractive force.   Is there an explanation based only on classical electrodynamics (say, at the level of Jackson). If not, is the explanation purely quantum mechanical?   Basically, how does one model this phenomenon?
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On RC circuit, capacitor discharges when the voltage supply is removed.  But I've learned that the net electric field outside a charged capacitor is zero by gaussian surface and gauss law.  I don't understand the mechanism. Shouldn't be there an electric field in order to make charge flow when discharging happens?  Is there an another mechanism?
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Faraday's law states that "Any change in electric field induces a magnetic field and vice versa". I don't see exactly where these fields are induced, but I assume that these fields are induced at each and every point in space.  Now, let us consider a charge Q, moving with a uniform Velocity V. Obviously this movement of the charge creates a change in the electric field everywhere. As such it should induce a magnetic field.  Subsequently, this change in the magnetic field should also bring about an electric field, an induced one, owing to further changes induced in the magnetic field.   Apparently this machinery seems to be similar to an EM radiation. But we know that an EM radiation can only be produced by charges in accelerated movement. Why this chain of events can't be seen as an EM wave propagation?
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I’ve been told that coulomb repulsion pushes excess electrons to the surface of a conductor (i.e. sphere) electrostatic equilibrium, and this symmetry causes the net electric field inside to be zero. However, why can’t excess charges just be evenly distributed throughout the sphere? Would that symmetry not cancel the fields from each charge?  It would be helpful if anyone can provide a diagrammatic answer.