Why is it so that a charged particle when accelerated radiates energy? I tried to think if it might be violating the law of conservation of energy but the energy transferred by the external agent may simply be absorbed by the electron and it can go on with increasing amount of kinetic energy  and it does not need to radiate energy.   There was another question on this website which had an answer that provided an account of this phenomenon in terms of field lines in some inner and outer ring. But, why should we consider field lines? They are merely paths of a charged particle which it will follow when left in an electric field.
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The  gives the recoil force, $\mathbf{F_{rad}}$, back on a charged particle $q$ when it emits electromagnetic radiation. It is given by:  $$\mathbf{F_{rad}} = \frac{q^2}{6\pi \epsilon_0 c^3}\mathbf{\dot{a}},$$  where $\mathbf{\dot{a}}$ is the rate of change of acceleration.  If a particle has a constant acceleration, $\mathbf{\dot{a}}=0$, then there is no reaction force acting on it. Therefore the particle does not lose energy.   Does this mean that a constantly accelerating charged particle does not emit electromagnetic radiation?
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Consider a photon is an energetic particle and therefore has a gravitational field. When a photon passes a molecule or particle of dust in space it will pull the dust towards it and deform the dust. This will lose energy in the normal Newtonian way, and the energy is supplied by the photon.   Assuming that the speed of light is constant this implies that the photon will become less energetic and therefore red-shift over its travels, simply as a consequence of interactions with near objects. Is the effect real and/or measurable?
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As I understand, light is what is more generally called "electromagnetic radiation", right? The energy radiated by a star, by an antenna, by a light bulb, by your cell phone, etc.. are all the same kind of energy: electromagnetic energy, i.e. photons traveling through space.  So far, so good? (if not please clarify)  On the other hand, there are these things called "electromagnetic fields", for example earth's magnetic field, or the magnetic field around magnets, the electric field around a charge or those fields that coils and capacitors produce.  Now here is my question:     Are these two things (electromagnetic fields and electromagnetic radiation) two forms of the same thing? or they are two completely different phenomena?   If they are different things, What does light (radiation) have to do with electromagtetism?   I'm not asking for a complex theoretical answer, just an intuitive explanation.
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Here are some depictions of electromagnetic wave, similar to the depictions in other places:      Isn't there an error? It is logical to presume that the electric field should have maximum when magnetic field is at zero and vise versa, so that there is no moment when the both vectors are zero at the same time. Otherwise one comes to a conclusion that the total energy of the system becomes zero, then grows to maximum, then becomes zero again which contradicts the conservation law.
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I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward.  What troubles me here, is the fact that it is traveling through space-time at the speed of light. Why is it at the speed of light?
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I have a problematic question for which I have been unable to attain a satisfactory answer. What is  truly?   -  I have read about how potential energy can be seen as the "highering" of an object within a field, be it gravitational, electromagnetic, etc.   In a way, an object is lifted to a higher position, and when it eventually falls down again energy is released back.  The object does not even have to be "lifted" beforehand, as with the case of asteroids.   However, since energy cannot be destroyed, it must somehow be stored, yet how does energy truly store itself within a field? It seems hard for me to grasp that energy can physically be stored within the positioning of an object?  I can't really get my head around how a field conserves energy within it. Kinetic energy on the other hand, can be, for me, intuitively understood, as the object really is "moving" and energy manifests itself through motion.  Can anyone elaborate on this, perhaps give reasoning as to why a field can in fact "store" energy? Please point out any fallacious or naive views I seem to hold.
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My textbook says that when a conductor is placed in an electric field, the electrons in it realign so that the net electric field inside the conductor is zero. There isn't a proof for this. It merely states that the electrons drift opposite to the applied electric field and create an opposite electric field inside the conductor canceling the external one.   I imagine Gauss's Law would provide a simple proof. If we try enclose a point inside the conductor in a gaussian surface, and note that the enclosed charge is zero, so the flux through the surface is zero and so is the electric field at the surface.   When I looked back at my reasoning, I realized that I had assumed that the charges induced on the conductor always stay at the surface, which I had no way of proving. How do I prove this formally?
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Let's say we have a emitter, emitting light that has frequency f, less than the threshold frequency of a metal.  If you leave light shining onto that metal, for long enough, does the energy of the individual photons accumulate, on the electrons, so eventually they will ionize, or does this not happen? What am I missing?
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The well known Larmor formula tells us that an accelerated classical charge radiates a power proportional to the square of the acceleration. It has been  that a charge in free fall in a gravitational field does not radiate. Since gravity is locally equivalent to acceleration, one may wonder whether a charge at rest in a gravitational field radiates. The  is that it does. However this radiation is not  to an observer in the same reference frame! Apparently, the radiation does not carry energy or momentum, or it would be observable, in this reference frame and this would mean that charged matter behaves differently from neutral matter in gravity.    How does unobservable EM radiation without energy and momentum make sense (Q1)?  Does the physical origin of charge acceleration determine whether radiation is observable or not (Q2)?  Is the answer to the question in my title "It depends?"?   Note added:  I did not find the discussion at  and  sufficiently enlightening.
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One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would collapse with the nucleus.  Now Schrödinger describes the electron as a wave function. His theory is able to describe all atoms (in contrast to Bohr's model), but how is the radiation problem solved? I understand that the wave has not an exact position in the time anymore. But the electron still "moves", so it has an acceleration anyway (because of vibrations or so).   Why is in this theory the electron not radiating anymore? And if it is, why doesn't the atom collapse?
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I was watching the Cosmos documentary where Neil deGrasse Tyson explained how certain energy photons get absorbed by an atom, which causes the electrons of that atom to climb into a higher energy state.  He then says that an atom produces a photon when those electrons drop to a lower energy state, but that we don't know why this happens. I understood that as 'we don't know what triggers this to happen'.  Is that true? And if so, are there any feasible theories that explain this phenomenon?
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In Synchrotrons I think they use microwaves to accelerate the electrons bundles that fly through-how does putting a microwave through a cavity accelerate an electron? I know that the Electric and Magnetic fields could and do have an effect on the electron, but if the radiation is moving parallel to the electron, wouldn't the force be perpendicular? Also, how exactly does the microwave radiation look in the vacuum chamber? Are the two ends constant nodes?
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As I navigate through physics stackexchange, I noticed .  Electrons radiate light when revolving around nucleus? Why is it so obvious?  Note that I do not know anything about quantum mechanics - and I just want classical stories.
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I am currently studying the motion of relativistic charged particles in electromagnetic fields. More exactly, we first derived the equation of motion in the 4-vector formalism.  I was a bit confused when my teacher talked about acceleration in special relativity. In which cases are we allowed to talk about it specifically in special relativity? (I mean that I have not studied general relativity yet) What stay constant ? Or are we making an approximation?  It may of course have a sense, though I have the feeling that in my courses, we only talked about constant speeds in special relativity.  I hope my question has a sense,  Isaac
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I've got a few questions on induction and electromagnetic fields. My current understanding of induction and electromagnetic fields is that, when electricity/current flows through a wire, it creates an electromagnetic field. If you twist that wire into a coil then you can concentrate that field. You can then induce current into a different coil by placing it inside of the electromagnetic field created by the first coil.  So here are my questions:  Q1. Does the electromagnetic field contain any energy?  EDITED QUESTION  Q2. Electromagnetic fields are the same as waves, so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field?   Q3. If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?  Q4. What spectrum of light are the electromagnetic waves that are in a field created by electricity?  Q5. Finally, why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing.   Thank you to anyone who answers.  Edited Q2: So my original question (although asked poorly) still stands. Where does the current that gets induced in the secondary coil come from? How does the electricity transfer from the primary coil to the secondary? For example, is it taken from the stored energy in the e.m field? Does the field just act as a bridge between the 2 coils? Or do the 2 coils exchange e.m waves which carry the electricity that is being transferred from coil 1 to coil 2? Or is it none of these things and something completely different?
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In the experiments for photoelectric emission, the light is incident on one face of the emitting plate, for example the anode, when determining the stopping potential. The electrons are emitted by this face of the plate. Why are the electrons emitted in the direction of the incident light, and not opposite to it?  I have read a little about photons (the key words being, a little), and from what i gather, they have an intrinsic momentum $p=h/\lambda$, which is transferred entirely to the particle that absorbs it (along with the energy $h\nu$). This should imply that the electrons try to move further into the cathode, and not escape it! What is the fault in the reasoning?  Thanks!
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I am sure there is a simple explanation for my confusion, but I am a little puzzled:  We are dealing with two parallel electron cannons that each produces a straight beam of electrons. They are placed at a distance d next to each other, which means there will be a repulsive electrostatic force between the electrons of the two beams. Also, according to the Maxwell equations, every moving electron will produce a magnetic field which then exerts another force on the other beam's moving electrons (similar to the effect that two currents in wires will cause an attractive force between the wires).   However, if we change the reference frame such that we are moving at the same speed alongside the electrons, there will be no magnetic field and no Lorentz Force. We are only left with the electrostatic force.  Do you guys know what might be the fallacy?