What is a magnetic field? (fun mental exercise)

[anorlunda]

SO - i was unable to accept that cat video. For me it's QV cross B in both cases. What'd i miss ??

Is there a handy link to that Einstein introduction, anorlunda ?

Too bad about the video, analogies are always imperfect. I couldn't follow your verbal thought exercise.

Jim, I think you would do better with the Susskind video linked in post #7. Susskind makes even the most exotic mathematics understandable by mere mortals. I learned it from Susskind; you can too.

Whoops, I forgot the Einstein link. Here it is.
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein wasn't the only one studying the EM riddles. There were many others. But he was the first to succeed because he abandoned the common sense definition of simultaneity. You must bring time into it to understand SR.

 

[jim hardy]

Thanks.. i made note of Susskind before we left but the laptop refused to connect to wifi until it got back home, will look at him tonight.

Sorry my words weren't clear. If Susskind doesn't clear it up i'll try to make a picture in Paint...

 

[meBigGuy]

If susskind clears it up, with all the 4-vectors. etc, then you are a batter man than I.

anorlunda:
My comments were not a comment on what you said about SR (which I accept wholeheartedly, since that's why I started the thread) but a comment on the "Scientific Basis of Electrical Engineering" not even mentioning SR.

 

[the_emi_guy]

still plodding along... (got back from that trip which interrupted my studies here, though i did muse a lot while driving cross country)

I'm okay with:
Take one charge and one observer. If there's relative motion between them then there's a magnetic field surrounding the charge. So two observers might report differently on the presence of said magnetic field.
But--
When i tried to work the positively charged cat video in my alleged brain, i got a "runtime error".
Here it is.
We have negative charge in motion due to the electron borne current in the wire, so a magnetic field surrounds it
When wire is stationary and +cat moves along it, there's relative motion between him and the field surrounding the wire's moving negative charge.
So +cat experiences F=QVcross B.
But when in the video, Mr +cat moves along in step with the negative electron borne charges in that wire, he no longer has relative motion wrt that negative charge.
Narrator asserted that in +cat's frame of reference, the magnetic field disappears because the relative motion disappeared.
I counter assert that +cat now has motion relative to the positive charges inside the wire which are moving wrt +cat from his nose toward his tail as he progresses along the wire.(or as it progresses under him).
Mr +cat sees j dot ds for positive and negative charges inside the wire that are not equal because of the tiny electron drift velocity, which narrator emphatically quantified as tiny relative to c.
By right and left hand rules, the magnetic field experienced by +cat from +charge (inside the wire) moving in direction from from his head to his tail
is the same as that experienced from -charge(inside the wire) moving opposite way in other reference frame.
The two reference frames yield the same magnetic field.

SO - i was unable to accept that cat video.
For me it's QV cross B in both cases. What'd i miss ??

Is there a handy link to that Einstein introduction, anorlunda ?

ALERT edited a bit to improve clarity

Jim,
In order for magnetic force to act we need both magnetic field (moving charges) and another charge moving relative to that field.
In the scenario: "cat moving and cat's frame of reference", you are right, the cat would see a magnetic field from the moving (+) charges (not mentioned by narrator) but there is no force because there is no charge moving relative to this field. Remember, from the cat's frame of reference his own charge is not in motion.

 

[jim hardy]

the cat would see a magnetic field from the moving (+) charges (not mentioned by narrator) but there is no force because there is no charge moving relative to this field. Remember, from the cat's frame of reference his own charge is not in motion.

Thanks !

i'm toggling that picture in my mind.
+cat sees the wire moving backward with respect to himself, because he and his reference frame are moving forward with the electron drift which is admittedly small but finite.
So - does +cat see those "Maxwell halos" of mmf (and flux) encircling the wire as stationary, or moving backward with the wire?

I know why I'm hung up - read Flatland as a kid.
Viewed from above those circles would appear straight lines , as do the men in Flatland
and the initial analogy of riding in a train planted the visual image of railroad tracks, where the ties are straight lines as are circles viewed from their own plane...
Viewed from a locomotive windshield the rail looks stationary(only because it's smooth) but the ties shoot by backward
and that's the visual image i affixed to those flux halos surrounding a wire..

So my question becomes
do those red B circles move along in direction of I with the moving +charges they encircle ? If so, they're moving backward in +cat's frame.
It would seem at first that they must - a single charge in motion would surely find itself surrounded by an accompanying "Maxwell Halo" .

Edit - added :
If that's so, then +cat sees relative motion between himself and those B circles ??

I'm sorry to appear stubborn - its just i need to reconcile this little point in order to progress. No mischief intended.

 

[the_emi_guy]

Jim,
In this case the B circles don't move. Constant current in a long straight wire creates a static magnetic field, analogous to the static E field between capacitor plates.
Motion of a charge relative to this static B field creates force.

The case of a single electron in motion is a different story. Here you will have a time & space varying set of E and H fields as the charge comes and goes.

It is the unique symmetry of the infinitely long straight wire with constant current that allows the "cat video" to nicely transform purely magnetic force in one frame of reference to purely electric force in another.

In the general case we will have time and position varying E and H fields in both frames of reference, and all of the math (Susskind, Feynman et al) shows us how to transform these fields between frames of reference.

 

[jim hardy]

Thanks. Makes sense, i figured the lone electron Coulomb had a different E-field...

I have homework to do now - those Feynman lectures, the Susskind video and the Einstein chapter anorlunda linked...

wont trouble you until have done more study..

 

[meBigGuy]

I think the key to this is that magnetic fields don't move as the wire moves along the axis of the current (even though that would explain the effects seen). The magnetic intensity remains the same all along the wire. Its not like a compass will see the longitudinal motion of the wire. Magnetic fields don't propagate. The field exists at a distance from the wire, and that field does not change as the wire moves.