Relativity & Moving charges - help?

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antandcharmi
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Relativity & Moving charges - help?

Postby antandcharmi » Sun Oct 23, 2011 8:20 am

I have a question involving the Maxwell chapter of Einsteinlight
http://www.phys.unsw.edu.au/einsteinlight
if anyone can help me with it I would very much appreciate it.

The chapter describes a thought experiment involving two like charges. An observer in the same inertial frame as the charges will not detect a magnetic force of attraction, whereas an observer past whom the charges are moving (or, I presume, an observer moving past the stationary charges?) will.

When the charges start moving, will they not also accelerate toward one another (assuming they are free to do so)?

If so, would the observer in the same inertial frame as the two charges see a displacement of the two towards one another (in whatever plane the charges are toward one another)? How would it appear to him, and why?

Alternatively, if the two charges do not accelerate toward one another, how would the observer past which they are moving, see their positions and the forces involved as they start moving?

Much thanks,
Anthony Rose

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joe
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Re: Relativity & Moving charges - help?

Postby joe » Sun Oct 23, 2011 11:13 am

An observer in the same inertial frame as the charges will not detect a magnetic force of attraction, whereas an observer past whom the charges are moving (or, I presume, an observer moving past the stationary charges?) will.

Correct. (And btw, these are symmetric and equivalent. When we say 'stationary', we mean with respect to the earth.)

When the charges start moving, will they not also accelerate toward one another (assuming they are free to do so)?

If the only forces between them were electrostatic repulsion and magnetic attraction, then they accelerate away from each other: the former is always larger. The observer who sees them as moving observes smaller accelerations because of the time dilation or (equivalently) because of magnetism.

In EinsteinLight someone holds the two charges in his hands. So there are extra, compensating forces that maintain the separation and the zero acceleration. These forces are ultimately electrical, so the same effects apply.

Joe

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Re: Relativity & Moving charges - help?

Postby antandcharmi » Mon Oct 24, 2011 8:33 am

Thanks very much for the reply, Joe.

The space in the question is very limited, so I could not set up a more precise scenario fully.

Assuming the charges are suspended in a static position by magnetic fields when at rest, but are free to move if another force acts upon them.

a) If the apparatus and train in which they are poised starts moving (at high but non-relativistic speeds), I assume the charges will experience a nett attractive force, and move closer to one another until the increase in replusive force balances the new attraction?

b) But wrt to an observer on the train, the charges are still stationary, and the gap between them will not change at all?

And the charges can be in any plane perpendicular to the direction of motion.

If the above is correct, then how do we reconcile the difference in the gap measured by the two observers? (I am not trying to find an error here, just trying to understand. Thank you!)

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Re: Relativity & Moving charges - help?

Postby joe » Mon Oct 24, 2011 8:52 am

Assuming the charges are suspended in a static position by magnetic fields when at rest

These magnetic forces are created by electric currents - i.e. by (other) moving charges. So the two observers will disagree over the speed of these moving charges and therefore the size of these magnetic forces.

If you want to work this out explicitly, I suggest that your new magnetic forces should be created by the simplest geometry possible.

Joe

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Re: Relativity & Moving charges - help?

Postby antandcharmi » Mon Oct 24, 2011 7:12 pm

Hmmm.... what if we stick the two balls onto the end of thin flexible rods, i.e. replacing your hands?

The rods can be stuck into the side of the train, one above the other. At rest, the rods flex upward until the tension balances the replusion. Both observers agree on the charges and tension.

i) When the train starts to move, the additional magnetic attractive force moves the balls closer together.

ii) BTW, if I zoomed down the station platform before the train started to move, this would have the same effect, from my perspective? Please forgive me if I am missing something obvious!

Thank you.

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Re: Relativity & Moving charges - help?

Postby joe » Mon Oct 24, 2011 9:32 pm

The flexible sticks - like my hands - are made of atoms and the forces that they exert are electrical (though they are variously called ionic, van der Waals etc). So, if the balls are stationary, then the total electrical force on each is zero.

Joe

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Re: Relativity & Moving charges - help?

Postby antandcharmi » Tue Oct 25, 2011 6:08 am

Yes, at rest, the balls are stationary?

When the train begins to move, the balls move with the train, and a magnetic force of attraction is generated as a result of the movement.

Therefore the moving balls will narrow the gap between themselves, until the new attractive force is balanced.

Would an observer on the train see the balls draw closer together, and how would he understand it?

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Re: Relativity & Moving charges - help?

Postby joe » Tue Oct 25, 2011 6:50 am

There would be no change in separation in the lateral direction.

The observer who sees the charged balls moving also sees movement in all of the other charges, including those in the hands/ stick/ whatever is keeping them stationary. So, all of the charges whose forces add up to zero are moving. The extra magnetic forces that appear when they are moving also add up to zero.

You can't simply separate out some of the electrical forces (that between the two balls) and apply relative motion to them, you have to consider them all.

If you want to work this out explicitly, I suggest that your new magnetic or electric forces should be created by the simplest geometry possible.

Joe

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Re: Relativity & Moving charges - help?

Postby antandcharmi » Thu Oct 27, 2011 9:41 am

Thank you, I understand what you are saying, but I am trying to create a simple geometry (please forgive me if I am not understanding you correctly) by suggesting that the balls be affixed to a stick. The stick could be any non-magnetic elastic medium, such as rubber, flexible enough to bend under the balls' magnetic force. Surely the sticks would not experience magnetic or electrical charge as a result of the train's movement?

Vetical cross-section of train (direction of train's movement is into or out of page):
________________
|<-Train's sides->|
| |
|---o | ---- = rubber stick, o = charged ball
| |
|---o |
_______________
[] [] <-wheels

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joe
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Re: Relativity & Moving charges - help?

Postby joe » Thu Oct 27, 2011 10:10 am

But when the sticks provide a force, that force is electrical, even if we call it ionic, van der Waals etc. So, leaving aside quantum mechanics for the moment, the extra forces they add are due to complicated distributions of charges. When the frame of reference is moving with respect to those sticks, we need to apply relativistic/ magnetic corrections to the forces. Which is difficult.

So, instead of using those complicated charge distributions (sticks), you should hold your balls in position with simple distributions, ie with other point charges, so that we can easily see what the new magnetic forces will be.

Calling them elastic sticks tends to hide the fact that you have put in a whole new bunch of electrical charges.

Joe

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Re: Relativity & Moving charges - help?

Postby antandcharmi » Fri Oct 28, 2011 1:31 am

I see. If we poise the charged balls in a simple magnetic field so they are at rest, then that field will also change with the movement, and I can bet that the result will be entirely understandable for the observer on the train, whether the balls move or not.
I am at this stage just trying to see what will happen, before I dig into how or why. My curiosity is focussed on *whether* both observers will see the balls move closer together. I would think they must do, because the formulae do not involve a change in relative distance in any plane perpendicular to the train's motion? Yet the lesson implies not?
Is this simpler: hang two like-charged wires close together from the ceiling. They do not hang straight down, but slightly apart.
Now, if the train begins to move, the observer on the platform sees the two wires move closer together, because they are moving. The observer on the train will see them move together as well? But why? (Unless he looks out the window! ;-) I suspect I am being dumb here.

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Re: Relativity & Moving charges - help?

Postby joe » Fri Oct 28, 2011 9:07 am

In no cases will the separation of the balls in the perpendicular direction change.

If you balance their electrostatic repulsion with magnetic forces, then the new magnetic force introduced when the charges move will be offset by the change in the magnetic forces when the system providing it moves.

If you balance it with electric forces, then the new magnetic forces will all cancel out.

You keep disguising the electric forces by calling them forces exerted by a hand, a stick or a string, but they are still electric forces because these objects are made of atoms. So, instead of these complicated electric geometries, I suggest that you explicitly describe the electric forces (just a few fixed point charges) or magnetic forces (some straight line currents) and work out the forces as in
http://www.phys.unsw.edu.au/einsteinlig ... e2_FEB.htm

Joe

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Re: Relativity & Moving charges - help?

Postby antandcharmi » Sat Oct 29, 2011 10:56 pm

Thanks Joe, I can barely follow the 'naive analysis' on the link because I don't have enough background. I did Physics 1 and Maths 1 in 1978! I feel like a tourist at a ski resort being shown how to do a ski jump. I get the idea, but I can't as yet question it or apply it to another example without spending weeks on it, which I don't have. But I remain intensely curious and if that is the only way I can understand it, I will.
But I get the idea that the charged balls will not move closer together because they are held in place by electro/magnetic forces subject to the same laws of physics.
I guess I misunderstood the video showing an instrument measuring difference in force between the two balls, and assumed that the increased force MUST equal acceleration if the balls are at first in balance when at rest. I forgot that there could be increased counter-force as well.
[out of space, another post following]

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Re: Relativity & Moving charges - help?

Postby antandcharmi » Sat Oct 29, 2011 11:15 pm

[continued]
The magnetic attraction is increasing on the balls, but the acceleration is zero because the electro/magnetic forces holding them in place also are affected by the movement. I presume the latter forces weaken until, at the speed of light, the balls experiencing no repulsion at all, the forces holding them in place will be exerting no pressure on them either.
In the two like-charged hanging wires example, gravity alone (no electro/magnetic forces?) prevents the wires from pointing directly away from each other. Where is the relativistic effect holding them in place during movement then?
And as an afterthought: if you're exerting physical effort to hold the charged balls in position and move near the speed of light, I presume you would still experience the same physical effort to hold them in place, even though they had virtually no repulsion force on them, because your muscles would experience the same 'weakening' (for want of a better word) effects?
Thank you for your patience!

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Re: Relativity & Moving charges - help?

Postby joe » Sun Oct 30, 2011 6:27 pm

The person holding the charges, or the machine that measures the force between them, both exert an equal and opposite force to the electrostatic one. In their own frame of reference, nothing changes. To an outsider, who sees them moving, there will be a new magnetic force between the charges, so the total force between them will be smaller. But this observer also sees the other forces as being reduced by the same amount. The reason for this reduction is that those forces, too, are electric, so they too produce magnetic forces that reduce them. (Or, if the measuring force happened to be magnetic, then it would get less by the same amount.)

In the formula for the Lorentz force, yes, the force goes to zero as the speed approaches c.

Joe


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