See post #76.
That gives me a formula but it doesn't answer the question for me. If you don't want to tell me just say you don't feel like figuring it out. jartsa was helpful but you are not
The formula answers the question. (I recognize your previously stated distaste for math, but it is undeniably essential for exactly this specific question and it does no good to berate someone for answering a mathematical question with math)
If you are asking us to check your working, post your working. If you are just guessing, all the tools are available on this thread for you to be able to answer your own question without guesswork. Try. Post your working or say where you get stuck.
I've just been told two co-moving electrons will not experience a magnetic force that pulls them towards each other. Is this true?? I thought this was like the main reason for two wires with identical currents attracting ...
It's hard to give a complete and correct description in words without math, but I'll say what I can. In a frame where the two electrons are moving, there is both an electric and a magnetic force. In a frame where the electrons are at rest (relative to the frame), there is only an electric force.
There are well defined transformation laws for how the components of the force transform, but it's hard to describe in non-technical language without mathematics. In technical language, we say that the forces transforms in a covariant manner.
In general, the difficulty in describe how things transformation when one changes frame is a limitation of your non-mathematical approach.
It's a bit like how length contraction works, but the details are different.
Didn’t we discuss this at quite some length earlier in this thread?
Yes, and from what I understood, your position was two co-moving electrons experience an attractive magnetic force towards each other. Or at least that's what I thought jartsa was telling me. And I thought I had it down until someone on another forum mentioned the argument I will elaborate on below.
The argument against this that was given me is if there is an attractive magnetic force and repulsive electric force in the frame where they are moving, but only a repulsive electric force in the frame where they are stationary, the frames do not agree on whether the electrons are moving towards each other or moving apart, or at least they don't agree on how fast they are moving apart. What is wrong with this argument? The only resolution I can think of is that the repulsive electric force in the frame where they are moving is stronger than it is in the frame where they are stationary, although I don't see why this should be the case that the electric force is stronger when the electrons are moving than when they are not.
They experience an attractive magnetic force in frames where they are moving and a repulsive electric force in all frames. The net force is repulsive in all frames
The frames all agree that the net force is repulsive. They do not agree on how fast they are moving apart
Also, why would you expect the electrons to move apart at the same rate as measured in different frames?
Ohhh the time is different for each frame now I see why that argument was wrong! Thank you
By the use of mathematics, it's possible to come up with a description of how the electrons separate using conceptual entities that stays the same regardless of frame. This simplifies the discussion enormously - and simplifies calculations, as well. These conceptual entities, called four-vectors.
However that description involves four-vectors - four-accelerations and four-velocities - which is something you didn't want to hear about as I recall, because it involved math.
The math to describe how ordinary velocities and accelerations transform is more complicated than the math that describes four-velocities and four-accelerations transform, as the later are easier to mainpulate. I'd probably mess up if I tried to do the math for how ordinary velocites transform unless I used the techniques I'm used to, which involve four-vectors. Conceptually it's possible, I suppose, one starts out with how distances and time transform (but that still requires the Lorentz transform, which is math), then one needs to go through more mathematical manipulations paying careful attention to which frame one is in to determine how velocities and accelerations transform. Finally, knowing how velocities and acceleration transform, one can discuss the dynamics, how the forces transform. But the math in this case tends to obscure the physics, because of the complexity of the transformations of ordinary velocities and accelerations as compared to their four-vector counterparts.
If we assume you still don't have the interest or background to talk about four-vectors, about all we can say is what we've said, which is that in some frames we describe the forces as having electric and magnetic components, and in other frames the magnetic components are zero. The components of the forces change when we change frames.
The simplest analogy I know of involves comparing changing reference frames to rotating maps. If we have a street-map, and we rotate it to crate a new map where north points in a different direction, in some conceptual sense the map is "the same map", even though we rotated it. But the components and the descriptions change. If one building was directly east of another building on the original map, it's no longer east on the new map, because the map has been rotated. The displacement has north-south and east-west components, on one map the north-south displacement is zero, on the other map it is not zero. But both maps describe the same territory.
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