If we consider two static charges in the space we know that they will experience a repulsion force according to Coulomb.  If the two particles are moving along the same direction at a fixed speed (like in a particle accelerator) the charges will start to produce a magnetic field that will attract each other. When the speed is relativistic enough, the two forces are almost compensated.  This is true in the frame of the lab, but what happens in the frame of the particles?  Two particles traveling at a fixed speed one next to the other do not see any magnetic field, only the electric, so how they justify the fact that the force disappear? In their frame the force is still present and they will not see it disappearing, but they will simply experience the usual Coulombian force. But when we do the change of coordinates between the laboratory frame and the particles frame the time will change according to the Lorentz transformations and it will slow down, slowing down also the effect of the electric force.  It is amazing that the time slows down at the same rate required by the magnetic field to compensate the electric field in the laboratory frame.  In other words we could say that the magnetic field is the expression of the time dilatation applied to the electric field. What do you think?
88220
As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the magnetic field produced by a current $I$ in an infinite wire. It's a relativistic effect; in the frame of a test charge, the electron density increases or decreases relative to the proton density in the wire due to relativistic length contraction, depending on the test charge's movement. The net effect is a frame-dependent Coulomb field whose effect on a test charge is exactly equivalent to that of a magnetic field according to the Biot–Savart Law.  My question is: Can  be derived using only  and Special Relativity?   If so, and the $B$-field is in all cases a purely relativistic effect, then Maxwell's equations can be re-written without reference to a $B$-field. Does this still leave room for magnetic monopoles?
65889
In pair production, two gamma rays with > .511Mev can come together to create a positron and an electron.    So two electromagnetic waves E and B fields, with No mass and No gravity and traveling at the speed of light,  can create two objects with Mass, with Gravity and with opposite E fields, and with NO B field.  Is there any theories on how E and B fields go about creating mass?  It seems the resultant objects both have opposite E fields, but the B field has vanished...where did it go?  In slow motion, as this happens, what exactly goes on to create mass from EM fields?  Can we use EM fields to manipulate this process further? i.e. change the rate of pair production?  Or to manipulate the G field of the resultant objects?
71799
I'm having trouble understanding the diagrams of elctromagnetic waves.  I have no problem with any concept in classical mechanics, and I think this can be answered without any relativity (which I don't know yet). I hope for an answer which is as intuitive as possible but any answer will be good.  So in the common diagram of an electromagnetic wave:     What exactly do the vectors represent? The wave is propagating though an eletromagnetic field. Are the lines just the field created by a particle?  We learned in physics that a charged particle creates a field in all of space, Is this a picture of changes in the field when it moves? And if so, how does it move? does it move up and down with the amplitude of this wave?  Lastly, It's not clear to me why the E-field part is not in the direction of the motion of the wave, because usually an electric field is depicted as so:    i.e it is in a direction "outwards" from the source of the charge.  This is really running through my mind for some time, so thanx for reading this!
43268
Assume that a particle is moving with four-velocity $u^\mu$ through a spacetime with metric $g_{\mu\nu}$ ($-+++$ signature).  Let us also assume that there exists a time-like vector field $t^\mu=(1,0,0,0)$.  Is it generally true that the energy $E$ of a particle is given by the following expression:  \begin{eqnarray*} E &amp;=&amp; -mt_\mu u^\mu\\ &amp;=&amp; -mg_{\mu\nu} t^\nu u^\mu\\ &amp;=&amp; -mg_{00}u^0\\ &amp;=&amp; -mg_{00}\frac{dt}{d\tau}? \end{eqnarray*}  In the special case that $t^\mu$ is a Killing vector and $u^\mu$ is tangent to a geodesic then $E$ is a constant of motion of the particle. But the energy of a particle need not remain constant in the general case - is that true?  If $E=-mt_\mu u^\mu$ is indeed the particle mass/energy then does it act as a source of spacetime curvature given that it depends on the $00$-component of the spacetime metric ifself? I suppose that is not a problem.
11443
Why does a moving (at constant velocity) magnet release more energy in the form of magnetic fields when the number of charges placed near it are increased? Say two current carrying coils $C1$ and $C2$ are in a system in which $C1$ is moving at constant velocity. The magnet fields from $C1$ will reach $C2$ after an interval of time. So at the moment $C1$ releases energy (M.F) it doesn't know about charges surrounding and it can't make predictions of how much energy is to be released at the instant. So it can only give out a fixed amount of energy in M.F.  Let's say it is equal to $M'$. When we add another coil say $C3$ in system, the amount of energy released by C1 is still $M'$. Therefore the total output can't exceed $M'$.  This statement says that you can't get more wireless energy by constant velocity gaining magnet in output even if you use many sets of coils.  But I think that it is false and we can get larger amount of energy as output by using extra coils. C2, C3, ... Cn Explain what is right
29610
I know plus pushes another plus away, but why, really, do they do that? On the other hand, molecules of the same type are attracted to each other. I find that weird.  I do know some stuff about four universal forces. But why in general the general "rule" is that opposite charges pull each other?   Yes, I do realize this could be connected to very basic stuff that science is still trying to figure out, and can be traced to the Higgs,  but still, there must be something to tell.
83329
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?
8363
Suppose I look at a parallel plate capacitor in its rest frame and calculate the electrostatic energy, $E$.  Next, I look at the same capacitor in a primed frame boosted in the direction perpendicular to the plane of the plates. In this frame, the $E$-field is the same strength, there is no magnetic field, and the volume over which the $E$-field extends is less by a factor $1/\gamma$. This suggests $E' = \frac{1}{\gamma} E$, but relativity states that energy transforms as $E' = \gamma E$.   Where is the missing energy?
85489
I understand how, and why, an accelerating charge emits radiation, and loses energy in the process, as well as the  formula for the power, and its derivation.  However, in classical mechanics, when we want to find the motion of a particle, the process is (theoretically) simple - find all forces on the particle as a function of position and time, plug in Newton's second law and solve the differential equation. It seems to me as if simply because a particle is charged, this process just ceases to work.  When talking about a charged particle, it is simply not enough to find all forces and solve Newton's law - now we need to somehow take into account the energy lost by the particle to radiation. However no one seems to mention how to take that into account, as a term in an equation of motion. It seems like all we know is the total power radiated by the particle - there is no concrete, complete description of how that loss affects its motion.  Of course, in some simple cases we can easily guess how the particle will be affected: for example, for an electron circling in a uniform magnetic field, it is obvious that energy loss due to radiation will cause the electron to spiral inward. You can, at least theoretically, write the Lorentz force acting on the particle, due to the uniform field, plug it into Newton's second law, and also write the Larmor formula, take that loss into account and find a complete description of the particle's motion.   However still, when we write simply Newton's second law here, with the only force being the Lorentz force, we find a circular, not spiral, solution; we have to synthetically add in the Larmor formula to truly recover the particle's motion. Contrary to classical mechanics where Newton's law is a complete description of the motion.   Why is Newton's law no longer enough, or put another way, what term am I missing that will fix the electron's motion, add an additional "force" the will cause it to spiral inward? Is there a general expression for that force? And how does one in general write the equation of motion for a charged particle (or a system of)?   I suspect the answer has something to do with the EM field changing not instantaneously but at the speed of light, since Newton's law of gravitation clearly yields stable, closed orbits and propagates instantaneously. Perhaps I should phrase my question this way:   How does the fact that the EM field propagates at a finite speed affect the way we have to write the equations of motion  for a charged particle (as opposed to the equations of motion for a massive particle, acted upon by an instantaneous, newtonian gravitational field)?   One last note: perhaps this has something to do with Maxwell's equations being Lorentz-invariant and not Galilean? However I find this unlikely to be the case since the electron doesn't have to move in a relativistic speed in order to experience this effect. In any case, this is also why I allowed myself to use Newton's second law and not its (special) relativistic expression - would using that fix the problem?
83318
I am trying to understand the idea of a force carrier with the following example.  Let's say there are two charges $A$ and $B$ that are a fixed distance from each other. What is causing the force on $B$ by $A$?  Classically charge $A$ has an associated electric field which causes a force on $B$. From the standard model, photons are the force carrier for the electromagnetic force. With this view does it mean that $A$ is constantly emitting photons but in a way that the magnetic component cancels out? If that is the case then doesn't that mean that charge $A$ is constantly losing energy?
121848
Experiments used to observe particle spin properties (such as ) rely on a varied magnetic field and a dipole-like reaction in the particle, deflecting it in one direction or another.  In the case of a point-particle such as an electron, how is it explained that a dipole with spatially separated poles exists in a single point?
19429
We can think that the electric field and the gravitational field operate similarly in the sense that the forms of their governing laws (namely, Coulomb's law and Newton's law respectively) are strikingly similar. The only difference one can point out is that while the electric charges come in two flavors, the gravitational masses come in just one.  Now, I have read that when a charged particle moves, the electric field lines associated with are distorted in a fashion because of the finite time required for the information about the change in the position of the charge to get propagated. And, I have led to the understanding that this is the cause of the existence of the magnetic field (and that if calculus is used it can be proven mathematically).   So (if this is true then) why doesn't the same thing happen to the gravitational field? Why is there nothing like a gravitational magnetic field? Or, is there?  Note  I have changed the language and the tone of the question massively. Although the question was fairly well received, I believe it was really ill-posed. As pointed out by ACuriousMind in the comment, the ''reason''described here behind the existence of the magnetic field is something that cannot be found a good support for. But still, due to the similarity between the equations describing their static behavior of electric and gravitational fields, one can still ask as to whether a boost would create some sort of a gravitational magnetic field if the original frame only had a static gravitational field. As the accepted answer points out, the answer is, roughly, a yes but the Maxwell-type equations for gravity aren't as well-behaved as are the original Maxwell equations of electromagnetism--one should note. In particular, the equations for gravity take the Maxwell-like form in appropriate weak limits only in some appropriately chosen gauges--and aren't Lorentz covariant.
60036
As everybody here knows, Maxwell's equation would look more beautiful if a magnetig charge were present. Beyond the aesthetics question, if a single magnetic Dirac monopole would be found, the consequence is that the electric charge would be quantized.  While, I guess, everybody should be happy with the news, my experimentalist background doesn't allow me to understand the experimental setting. I therefore ask for the following advice -- a rather theoretically oriented question.  A recent paper,     Observation of Dirac monopoles in a synthetic magnetic field. M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen and D. S. Hall. .   claims to have observed such monopoles.   Can somebody shed light on the theoretical implicacions of this work? Concretely, should we now take care before saying that it's been proven that the electric charge is quantized?
31787
I've heard that special relativity makes the concept of magnetic fields irrelevant, replacing them with relativistic effects between charges moving in different velocity frames. Is this true? If so, how does this work?
29339
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?
11743
I'm tutoring high school students. I've always taught them that:     A charged particle moving without acceleration produces an electric as well as a magnetic field.   It produces an electric field because it's a charge particle. But when it is at rest, it doesn't produce a magnetic field. All of a sudden when it starts moving, it starts producing a magnetic field. Why? What happens to it when it starts moving? What makes it produce a magnetic field when it starts moving?
103221
According to my text book:  The Lorentz Force F on a charged particle moving in an electromagnetic field is given by:  $$F= qE + q(v\times B)$$  then it states that "it is to be pointed out that only the electric force does work, while the no work is done by the magnetic force which is simply a deflecting force."  How can this by true won't the the magnetic force have a considerable magnitude, will it now impart kinetic energy to the charge? Any explanations will help a lot. Please keep the terminology simple, thanks.