How do magnetic fields turn into electric fields at relativistic speeds?

[Wannabeagenius]

Hi All,

I'm reading about special relativity but I'm having a very difficult time trying to understand what the author is saying.

Imagine a very large magnet mounted by railroad tracks such that a moving train passes through it. On a moving train is a loop of wire. Now as train passes through the magnet, a current is induced in the wire.

Apparently their is a difference if you are observing this loop from the ground or from the train but I don't see the difference. A loop is moving through a magnetic field and an emf gets generated. From anybody's point of view, the time rate of change of magnetic flux through the coil is changing.

Please tell me what I am missing?

Thank you,
Bob

 

[0xDEADBEEF]

If the loop is parallel to the tracks (sideways), and the magnet is across then this is true for geometric reasons.

For the person on the train it looks as if the loop has the area A_L and the Magnet has the area \gamma^{-1}A_M if it contains the same flux, then the flux density is higher. A higher Flux density in a smaller area through a larger loop should give a stronger emf.

From the ground the the loop has the area \gamma^{-1}A_L whereas the Magnet has the Area A_M so you have the Field more spread out and you capture less field due to the smaller loop, so the emf should decrease.

Is this reasoning in line with your book? Which book are you reading?

Sorry, the TEX function is broken today...

 

[Wannabeagenius]

If the loop is parallel to the tracks (sideways), and the magnet is across then this is true for geometric reasons.

For the person on the train it looks as if the loop has the area A_L and the Magnet has the area \gamma^{-1}A_M if it contains the same flux, then the flux density is higher. A higher Flux density in a smaller area through a larger loop should give a stronger emf.

From the ground the the loop has the area \gamma^{-1}A_L whereas the Magnet has the Area A_M so you have the Field more spread out and you capture less field due to the smaller loop, so the emf should decrease.

Is this reasoning in line with your book? Which book are you reading?

Sorry, the TEX function is broken today...

Hi And thank you for your reply.

I'm at the very beginning of Chapter 12, Electrodynamics and Relativity of the book "Introduction to Electrodynamics" by David J. Griffiths.

What he is saying here has nothing to do with the orientation of the hoop. It seems to me that it has to do with the perception of whether the current induced in the coil is due to an electric or a magnetic field.

The problem I'm having is that I don't see any difference between the two viewpoints. To me, it's simply a magnetic field issue and the magnetic flux through the hoop changes with time as the train moves forward. And this seems to be the case from a person on the train or a person on the ground.

I know I am wrong!

Bob

 

[Okefenokee]

Picture a charged particle moving along an infinite current carrying wire at a modest non-relativistic speed. The particle sees a magnetic field that will cause it to be attracted to or repelled from the wire. The wire sees an electric field from the particle.

Now imagine that the particle is accelerated to 99.99999...% of the speed of light and the current in the wire is turned off. From the particle's perspective, the wire is zipping by at near light speed. The wire also appears to be contracted.

Now if we turn the current on in the wire it will travel at some speed in the opposite direction of the particle. It cannot appear from the particle's perspective that the current of moving charge in the wire is moving faster than light. The speed of the current's charge carriers in relation to the wire must appear slower from the particle's point of view than from the wire's point of view. Slower current flow means less magnetic field. The current will appear to be bunched up and contracted more than the wire itself because relativistic effects like contraction will ramp up exponentially with speed. If the charge carriers appear to be bunched up then the wire will appear to have a net charge. In other words, the fast moving particle will see less magnetic field and more electric field from a current carrying wire.

Note that the particle is still either attracted to or repelled from the seemingly charged wire just as it was before. Conversely, the charged particle's electric field appears to change into a magnetic field from the wire's perspective because moving charges make a current. That's the effect in a nutshell. Magnetic fields become electric fields and vice versa. You may have to draw some diagrams to see how they orient to one another (they should be perpendicular in all cases... I think).

The loop situation is beyond my powers of visualization for the moment on this sleepy Sunday morning.

 

[sophiecentaur]

"To me, it's simply a magnetic field issue"
I think that's your problem; you have to discard views like that if you are going to 'get' relativity. There's always something else involved - just like when one 'assumes' that velocities just add up and then you find that they can't ever add up to c.

 

[0xDEADBEEF]

Sorry I could not find an online version of that book. The main point is, that magnetic fields turn into electric ones and vice versa, under relativistic boosts. So the observed effects stay the same. This is obvious when you regard a charge flowing with some speed v. When you travel along the wire at the same speed, you won't see a magnetic field anymore but a static one, because from your point of view the charges don't move.

I am sorry but I cannot elaborate unless I see the chapter in question.

 

[Okefenokee]

Ahh, I think I have the answer for this, maybe. It just popped into my head. Like the guys here are saying, magnetic fields turn into electric fields at r-speed (relativistic).

If you have a magnetic field, B, it will turn into an electric, E, field. The E field will be curled around the B field just like a B field curls around a current. It will be sort of circular. The Maxwell-Faraday equation says that if an E field is curled then there must be magnetic flux present: d/dt(B). (http://en.wikipedia.org/wiki/Maxwell's_equations#General_formulation").

In the low speed case, the loop picks up the flux directly from B as it passes by. In the high speed case, the loop gets the flux indirectly from B through the curled E field that it senses.