In a uniform perpendicular magnetic field , force on charged particle cause change in direction of momentum. How do we explain it using conservation of momentum?  I don't know what is Hamilton or canonical or something like that.
124191
is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand.  Considering a particle moves in a magnetic field with charge $q$ and mass $m$, its hamiltonian is $$H=\frac{\vec{P}^2}{2m}=\frac{(\vec{p}+q\vec{A})^2}{2m}$$ where $\vec{p}$ is the momentum of the particle, $\vec{A}$ is the vector potential of the magnetic field and $\vec{P}$ is the canonical momentum of the particle.  I think, because of the expression of the hamiltonian, the canonical momentum $\vec{P}$ is a conserved quantity.  But by the answer in , it seems that the canonical momentum is not conserved even in a simple example that a particle moves in a homogeneous magnetic field.  I am confused about this question. Is the canonical momentum conserved when a particle moves in magnetic field?
79130
Can anybody please tell me if magnetism is a conservative force or if there is a field associated with it? How to reason? One thing I know is that the work done by a magnetic force is equal to $0$.
82475
Motivating the non-relativistic momentum $$\mathbf{p} = m\mathbf{v}$$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and should be proportional to velocity (how fast and to where it is moving). Now, in Special Relativity the momentum changes. The new quantity of motion becomes $$\mathbf{p} = \dfrac{m\mathbf{v}}{\sqrt{1-\dfrac{v^2}{c^2}}}$$ Or, using $\gamma$ the Lorentz factor $$\mathbf{p} = \gamma(v) m\mathbf{v}$$ where I write $\gamma(v)$ to indicate that the velocity is that of the particle relative to the frame in which the movement is being observed. The need for this new momentum is because the old one fails to be conserved and because using the old one in Newton's second law leads to a law which is not invariant under Lorentz transformations. So the need for a new momentum is perfectly well motivated. What I would like to know is how can one motivate that the correct choice for $\mathbf{p}$ is the $\gamma(v)m\mathbf{v}$. There are some arguments using the mass: considering a colision, requiring momentum to be conserved, transform the velocity and then find how mass should transform. Although this work, it doesn't seem natural, and it is derived in one particular example. On my book there's even something that Einstein wote saying that he didn't think it was a good idea to try transforming the mass from $m$ to $M = \gamma(v)m$, that it was better to simply keep $\gamma$ on the new momentum without trying to combine it with the mass. So I would like to know: without resorting to arguments based on transformation of the mass, how can one motivate the new form of momentum that works for special relativity?
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?
121403
Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, Halliday &amp; Resnick's Fundamentals of Physics, Taylor's Classical Mechanics, and ultimately the Feynman lectures (mirrored by Caltech). Hopefully this gives somewhat of a feel of my level of physics understanding so as to avoid any answers that fly far above my head.  As I've understood from previous reading of electromagnetism (for example, in Halliday), a point charge is not affected by its own electromagnetic field. Unfortunately, as I recently read in the Feynman lecture on electromagnetism, :     For those purists who know more (the professors who happen to be reading this), we should add that when we say that () is a complete expression of the knowledge of electrodynamics, we are not being entirely accurate. There was a problem that was not quite solved at the end of the 19th century. When we try to calculate the field from all the charges including the charge itself that we want the field to act on, we get into trouble trying to find the distance, for example, of a charge from itself, and dividing something by that distance, which is zero. The problem of how to handle the part of this field which is generated by the very charge on which we want the field to act is not yet solved today. So we leave it there; we do not have a complete solution to that puzzle yet, and so we shall avoid the puzzle for as long as we can.   At first I figured I must've misunderstood, but upon rereading, it's clear Feynman states the that electromagnetic field due to a point charge does, in fact, influence said charge; I inferred this "self-force" must be somewhat negligible for Halliday to assert otherwise. What stood out to me was that Feynman states this problem had not yet been solved.  I suppose my first major question is simply, has this problem been solved yet? After a bit of research I came across the  which appears to refer exactly to this "problem of self-force". As the article states the formula is entirely in the domain of classical physics and a quick Google search indicates it was derived by Abraham and Lorentz in 1903-4, why is it that Feynman state the problem was still unsolved in 1963? Has it been solved in the classical case but not in QED?   Lastly, despite the Wikipedia article , is this problem of self-force present with other forces (e.g. gravity)? I believe it does state that standard renormalization methods fail in the case of GR and thus the problem is still present classically, though it does mention that non-classical theories of gravity purportedly solve the issue. Why is there not a similar Abraham-Lorentz-esque force possible in GR -- is there an underlying fundamental reason? Due to the relative weakness of gravity, can these self-force effects be ignored safely in practice?  I apologize for the long post size and appreciate any help I can receive. I only hope my post isn't too broad or vague!
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?
118255
A charged particle moving with an acceleration produces electromagnetic waves. Why doesn't a charged particle moving with a constant velocity produce electromagnetic waves? As far I understand, the electric and magnetic fields in space will still be time-dependent, if a charged particle is moving with constant velocity, so they could have given rise to electromagnetic waves, but they don't.  Also, why do accelerating charged particles produce electromagnetic waves? What is Nature's intention behind this phenomena?
40662
I have been reading about the electric field induced on a metal ring due to an increasing magnetic field directed along the axis of the ring and the electric field lines are found to form concentric circular loops. This implies that the electric field formed is not conservative. Why is it so? Are electric field due to free charges and those due to changing magnetic field two entirety different  things?  Please provide an intuitive and less mathematical explanation as I am just a high school student with knowledge of basic calculus.
121578
We can achieve a simplified version of the Lorentz force by $$F=q\bigg[-\nabla(\phi-\mathbf{A}\cdot\mathbf{v})-\frac{d\mathbf{A}}{dt}\bigg],$$ where $\mathbf{A}$ is the magnetic vector potential and the scalar $\phi$ the electrostatic potential.  How is this derivable from a velocity-dependent potential  $$U=q\phi-q\mathbf{A}\cdot\mathbf{v}?$$  I fail to see how the total derivative of $\mathbf{A}$ can be disposed of and the signs partially reversed. I'm obviously missing something.
48139
A permanent magnet produces lines of magnet flux that we call a "magnetic field".  Those lines come from inside the magnet, come out of the N pole, loop outside the magnet, &amp; return back into the S pole to complete a magnetic circuit.  Using ferromagnetic materials, other magnets, &amp;/or test equipment, we feel &amp; measure forces that are caused by a magnet/s when other materials are placed within close enough proximity to the magnet/s (i.e. within their magnetic field/s).  We therefore conclude that the magnetic lines flow in a specific direction &amp; exert definite forces (i.e. magnitudes/strength) on some materials (ferromagnetic &amp; other magnets), depending on where those materials are placed within the magnetic field of a magnet/s.    We label those forces as "H Field" &amp; "B Field". We measure H in terms of Amperes/meter. We measure B in terms of Newtons/meter/Ampere (or Tesla). We also commonly defined B in terms of the force that it exerts on moving electric charges (i.e. the Lorentz force).  An "Ampere" is basic unit of electrical current in the SI system, which = 1 Coulomb per second--which is formally defined to be the constant current which if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed one meter apart in vacuum, would produce between these conductors a force equal to 2 × 10 −7 newton per meter of length.  A "Coulomb" is the standard unit of quantity of electricity in the SI system, which = the quantity of charge transferred across a conductor in which there is a constant current of 1 Ampere/Second.  Consequently, those "magnetic lines" are currents (or flows) of charges that don't appear to need any external source of energy to continue generating their currents.  We also know those magnetic lines exist inside a vacuum, so they are independent of air molecules to flow outside of a magnet.  So now my questions:   Exactly what charged particles are flowing outside (and inside) a permanent magnet that create the magnetic "lines"?   Do those particles come from something inside the magnet or does the magnet do something outside of it to affect unknown particles to make the lines? If there is a current (i.e. a continuous flow of charged particles), then why don't we harness that current like a water wheel (instead of 'using energy' to rapidly move copper wires through magnetic fields--like we do with electricity generators?)  Shouldn't we be able to get the line currents to charge a capacitor (or or other device) &amp; then otherwise discharge the capacitor for the energy that we want?
43205
I'm a physics tutor for 11th and 12th grade students. I taught my students that momentum is conserved only when the net external force on the system is zero. But in the books we are following, momentum was conserved in the following cases in spite of presence of an external force:   A body (mass m1) is dropped from a tower (height h) and another body (mass m2) is projected vertically upward with initial velocity u. Find the velocities just after collision. (Gravitational force is the external force) Two bodies projected towards each other on a rough table surface, with all required parameters given asked to find the velocities after collision. (frictional force is the external force) Body explodes in mid air. Momentum is conserved before and after explosion. (Again gravitational force is the external force)   I explained to my students in all these cases though an external force is present it has negligible effect. But I'm not satisfied with my answer.  EDIT: Thank you for the comments and answer. It is clear that contribution of external force to change in momentum is negligible. Can someone do the calculation of taking change in momentum into consideration and showing that it is negligible?
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?
110875
I have read these questions:              where it says:     A spinning charged particle constitutes a magnetic dipole. Its magnetic dipole moment μ is proportional to its spin angular momentum S:   μ=γS   the proportionality constant γ is called the gyromagnetic ratio.     where the comments say:     Because in a magnet, the atomic electrons are moving around their respective nuclei constituting a dipole and the dipoles are aligned in same direction to give net magnetic dipole moment.    So one is saying that magnetic dipole moment is caused by spin angular momentum, which is the intrinsic spin of an electron, the other one says that magnetic dipole is cause by electrons orbiting (orbital angular momentum) the nuclei (of course as per QM they are not classically orbiting).  So which one is right?  None of these questions says whether the magnetic dipole moment at QM level is caused by the intrinsic spin of electrons or the bound electrons' (OAM) orbiting (as per QM existing at a certain energy level) around the nuclei.  Question:   Which one is right, is the magnetic dipole moment as per QM caused by the intrinsic spin of electrons or by electrons orbiting (OAM) the nuclei existing around the nuclei at a certain energy level?
16675
I heard that a magnetic field only creates a force on a moving charge, not a stationary one. However, what if the solenoid containing the magnetic field was moving through a stationary charge. Would that create a similar force? Thanks!
23838
The Lorentz force on a charged particle is perpendicular to the particle's velocity and the magnetic field it's moving through. This is obvious from the equation:  $$ \mathbf{F} = q\mathbf{v} \times \mathbf{B} $$  Is there an intuitive explanation for this behavior? Every explanation I've seen simply points at the equation and leaves it at that.  I can accept mathematically why $\mathbf{F}$ will be perpendicular to $\mathbf{v}$ and $\mathbf{B}$ (assuming the equation is correct, which it is of course). But that doesn't help me picture what's fundamentally going on.  Trying to create an analogy with common experiences seems useless; if I were running north through a west-flowing "field" of some sort, I wouldn't expect to suddenly go flying into the sky.  I'm hoping there's a way to visualize the reason for this behavior without a deep understanding of advanced theory. Unfortunately, my searching for an explanation makes it seem like something one just has to accept as bizarre until several more years of study.
24909
In the textbook I'm reading it gives an example of where a person pulls a rectangular wire with a velocity $v$ and the left side of that wire is in a uniform magnetic field.    After some calculations, the author states that calculating the emf from the current induced in line $ab$ is equivalent to the work done by the person pulling the wire even though the force of the magnetic field has no effect on the work done by the person and the force exerted by the person has no effect on the emf. How is that the force produced by the magnetic field can produce an emf on line $ab$ if magnetic fields do no work?
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!