On the Electrodynamics of Moving Bodies

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It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.


A given statement is told in literature of Albert Einstein ,but I don't find any explanation so I like if anyone can explain us,by help of maths or even by flux line etc
 

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Born2bwire
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It kind of goes back to special relativity in that all observers should agree on the physics of a problem. So we have a problem where we have a magnet and some conductor that are initially stationary. If we fix our observer in the conductor's frame and move the magnet, then we observe a time-varying magnetic field. Via Maxwell's equations this means that there is also a time-varying electric field. This electric field exerts a Lorentz force on the charges in the conductor causing them to move, thus exciting currents.

Now we fix our observer on the magnet and observe the same movement of objects. But this time, from our new observer's point of view, it is the conductor that moves. Now we only see a static magnetic field so how can we observe the same induced currents on the conductor if there is no electric field to act on the conductor's charges? The answer is that since the conductor is moving, the conductor's charges are also moving. Moving charges experience a Lorentz force due to any applied magnetic fields. Thus, the stationary magnet's static fields apply a Lorentz force on the conductor's moving charges and thus induce currents.

It turns out, as is necessary, that the induced currents in either case are identical.

No biggie here but now let us consider the problem where there is a spatially non-varying magnetic field. When we have a magnet, its field has to be spatially varying and so we know that movement through the magnet's fields, from the viewpoint of the conductor, must appear time-varying. But what happens if the magnetic fields are spatially constant? Then the movement through the fields does not result in a time-variation. However, from the lab frame where we see a moving conductor we have the same physics as before. That is, the charges on the conductor are moving through the static magnetic field and can experience a Lorentz force that induces a current. But how can we see the same thing happening from the conductor's point of view if we no longer have a time-varying magnetic field that has an associated time-varying electric field?

This is where special relativity comes into play by allowing us to realize that the electromagnetic fields have to undergo a Lorentz transformation. We can derive (and technically Maxwell's equations satisfy special relativity already, one just needs to work out the transformations) the Lorentz field transformations and find that a magnetic field can transform into an electric field when we go to a moving frame. So because the conductor is in a moving frame relative to the purely magnetic field frame, there can be a transformation of the magnetic field into an electric and magnetic field. This electric field will induce the same currents as before.

EDIT: Uh oh... looks like this got moved into the SR forums... Be gentle...
 
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A given statement is told in literature of Albert Einstein ,but I don't find any explanation so I like if anyone can explain us,by help of maths or even by flux line etc
Basically, Einstein was thinking about something like moving a bar magnet through a loop of wire. The fields etc. are very different if it is the magnet or the loop that is stationary, but in the end the induced EMF measured in the loop is the same. This is all that he is talking about.
 
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Shah:
good question...as noted above, there are subtle differences among early all observers. Another one is the pole (or ladder) in the barn paradox, or Einstein-Podolsky-Rosen paradox....or which observer "see's" the effects o the horizon surrounding a black hole and which doesn't (stationary and free falling,respectively). The universe is NOT what it appears on the surface.

http://en.wikipedia.org/wiki/Barn-pole_paradox

Relativity suggests different observers may make different measurements of sorts, such as in length and passage of time, but all will agree on the order that things happen...that is, causality (cause and effect) is not violated. Whether quantum mechanics ruins causality is generally not thought to be true, but seems open to some debate.

At the heart of your question is the dual nature of an electromagnetic field....viewed from one perspective, an observer (stationary) "sees" an electric field while another (moving) observer sees a magnetic field.....but that's no more crazy than different observers measuring,say, different passages of time.

You'll find some interesting observation descriptions here,
http://en.wikipedia.org/wiki/Magnetic_field

but I doubt it will precisely provide the answer you seek....all we have is observations and mathematical descriptions, not a truly insightful fundamental understanding.

My own novice conclusion is that the above "paradoxes" will be understood only when we understand the relationship between mass forces,time, energy and space. They all popped outof a bang, apparently, and so all are related. So far all we have "unified" are the weak,strong and electromagnetic forces....and we have more to learn about those three as well.
 

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