Why do electrons obey Fleming's left hand rule?

[Khashishi]

You are not alone. I still have not found any logical explanation, only "That's just the way it is." Just to be clear the simplified question is "Why is the force up and not down" as in this image... it logically could be either direction.
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I thought I already settled that part of the question in my previous answers. Is there something missing in the explanation?

A bar magnet is not symmetric with respect to a mirror image. The magnetic field is due to unpaired electrons with aligned spins. If you take a mirror image, you flip the spins, and therefore you flip the north and south ends (which we call + and - due to convention). This is analogous to taking a mirror image of your windmills. The blades change pitch direction. When you take a mirror image, you must reverse the direction of the magnetic field.

 

[jerromyjon]

I thought I already settled that part of the question in my previous answers. Is there something missing in the explanation?

I am not the OP, although I have asked this same question and have gotten similar explanations in the past. I am still not clear on the reason which may be simple and I still just don't get it. I assure you it is not because I am dense or an idiot, I just don't do advanced math.

A bar magnet is not symmetric with respect to a mirror image.

That may or may not be the point I am missing, but I cannot find any further reading to make sense of it. I have found some pay-walled papers from 2015 and newer so this I think is stuff I have missed in my years of searching for a better understanding!

 

[jerromyjon]

It is equally known that the direction depends on the sign of the charge. Both is just observation. Why is the latter more difficult to accept?

Because I don't understand the geometry of the signs of the magnetic field and the force apparently. The sign of the current carrying conductor is obvious in the illustration. The sign of the force pointing up leads me to believe the up direction is positive and the down direction is negative. I must not have a good understanding of the magnetic field.

 

[jerromyjon]

Now, this "transformation" isn't as simple as I have stated above, but this is the origin of why magnetic field can exert a force on a charge particle, and why it will only occur if (i) the charge is moving and not stationary in the field, (ii) it does not move parallel to the direction of the magnetic field.

(ii), this is the part I think where it gets difficult to understand. Is there any way to visualize "parallel to the direction of the magnetic field"? Or perhaps just elaborate on this part?

If you want the explanation and see where your left-hand/right-hand rules come from, then I welcome you to go look at Maxwell equations and learn about vector calculus. THOSE are your "explanations".

If that is the last word then fine, nuff said. I will try to learn it and explain it in laymen's terms to all else who wonder.

 

[Khashishi]

I still think you are getting worked up about the vector representation. We use the same vector representation for angular momentum. If the rotation is in the x-y plane, we say the angular momentum vector is in the z direction. The sign determines if the rotation is counterclockwise or clockwise looking down the z axis. (This is by convention--there is no physical reason for it.)

Why is motion in the x-y plane result in angular momentum in the z direction? This is just due to our choice of representation. There's nothing physical going on. Similarly, a magnetic field in the z direction has nothing to do with motion in the z direction. It is due to a current loop in the x-y plane. Therefore, it induces a force in the x-y plane, trying to bend the trajectory into a circle.

If this is not your difficulty, you'll have to be more clear about what is.

(We call angular momentum and magnetic field "pseudovectors" because they aren't really vectors, but representations of oriented surfaces.)

 

[jtbell]

A Google search for "derivation of Lorentz force law" led me to a fairly recent paper (within the last 15 years) by J. H. Field:

https://arxiv.org/pdf/physics/0409103.pdf

The math is surely above the OP's level, but the introduction may nevertheless make for interesting reading. The question "why is the magnetic force law the way it is" is a rather deep question, and it turns out you have to use relativity and some assumptions in order to "answer" it.

 

[jerromyjon]

Yeah, I think I'm an idiot now...

 

[jerromyjon]

The math is surely above the OP's level, but the introduction may nevertheless make for interesting reading. The question "why is the magnetic force law the way it is" is a rather deep question, and it turns out you have to use relativity and some assumptions in order to "answer" it.

Yeah, It is easier than that.

 

[jerromyjon]

We use the same vector representation for angular momentum.

Thanks. That analogy, it was what "clued me in". That seems like why chiral fermions is a problem, as well. I might be jumping off a ledge, but it seems applicable...

 

[tech99]

You are not alone. I still have not found any logical explanation, only "That's just the way it is." Just to be clear the simplified question is "Why is the force up and not down" as in this image... it logically could be either direction.
View attachment 215014

My previous post explains in terms of electrostatics why it happens that way.
If you have a wire carrying a current, it contains moving charges. If another charge tries to approach it at right angles, it finds itself dragged along by the current. This occurs because of electrostatic action combined with some simple Relativity.

 

[jerromyjon]

To detect a magnetic field then you need something else in your empty space.

And now with two other aspects (a current carrying conductor, and an EMF), I have a sense of the angular relationship to have a more intuitive understanding of the magnetic field.

I am indebted to "jartsa" in yesterday's Classical Physics for bringing the above paper to my attention.

As I am as well to the both of you. I bookmarked it for further study. :-)

If the answer is yes then another angle to the question is how this magnetic field knows to curve in a particular direction.

Simply by charge. An electron goes one way and a positron goes the other. Can you follow the rotation to determine which is which because I still get confused...