Why do electrons obey Fleming's left hand rule?

[mmanyevere]

What physical attribute of the electron causes it to experience force in one direction and not the other when it moves in a magnetic field?

As a crude analogy, when wind blows in the face of a windmill, we can intuitively see why it rotates clockwise or counterclockwise. It is because of the way the blades are twisted and the fact that the windmill is anchored. We can also easily see how reversing the wind direction will also reverse the rotation of the windmill. Is there some similar intuitive explanation as to how the electron interacts with the magnetic field so that it experiences a force at right angles to its direction of motion (and that of the magnetic field) and why that force is in a certain direction and not the opposite? If you threw a perfectly spherical ball in the wind, it can only experience a drag that slows it down. Does the electron have some deformity in its shape that causes it to always behave the way it does?

I read that when an electron is moving away from the viewer, it induces a circular magnetic field in the direction that a corkscrew would have to turn in order to burrow into the wood. If we imagined the electron to be such a screw, I am seeking an understanding how the electron can always know to align itself in such a way that its tip is in front. Since the electron is not anchored to anything, there would be nothing to stop it from pointing in all manner of directions and if the screw would point backwards it would experience a force in the opposite direction from what we expect from Fleming's left hand rule.

 

[BvU]

Hello mmanyevere,

What physical attribute of the electron causes it to experience force in one direction and not the other

Its charge does.

The electron has a antitwin, the positron. Same particle, opposite charge. That one goes exactly the other way.

Of course you can now repeat the question: why does one of the two go left and the other right ? The answer is outside the realm of physics. We observed it and that's it, period.

 

[mmanyevere]

Of course you can now repeat the question: why does one of the two go left and the other right ? The answer is outside the realm of physics. We observed it and that's it, period.

Thank you for the quick response. Not sure if the why part is outside the realm of physics or just something not understood yet. To go back to my windmill analogy, would it be enough to simply state it as an observation that when the blades are twisted in a certain way, the windmill rotates in one direction and vice versa? Clearly the physics is understood a lot better and we can give a detailed explanation of why the windmill rotates clockwise or anticlockwise. I am just looking for such an understanding beyond the observation as to why the positron goes left and electron right.

 

[Khashishi]

The choice is due to convention and history. People can't directly see the magnetic field, so we historically chose an arbitrary sign for "north" and "south". We could easily have chosen the opposite sign, in which case we would use a right hand rule.

 

[mmanyevere]

The choice is due to convention and history. People can't directly see the magnetic field, so we historically chose an arbitrary sign for "north" and "south". We could easily have chosen the opposite sign, in which case we would use a right hand rule.

Maybe the topic of my post does not speak to exactly what I wanted to ask. The question is not about why it's called the left and not the right hand rule. It's about how the electron, when moving in a magnetic field is always forced to one particular side and not the other. When we magnify the electron, it probably looks spherical and identical from all directions. How then does the charge inside (or on) it cause it to swerve to one side always? The issue would not be as vexing to me if the electron was swerved in the direction of the magnetic field (either up or down). Because the electron looks like a perfect sphere (maybe I'm wrong on this) and is not anchored to anything, it just looks equally possible that it would go to the left or to the right but it always chooses one side. How can we intuitively explain this?

 

[ZapperZ]

Maybe the topic of my post does not speak to exactly what I wanted to ask. The question is not about why it's called the left and not the right hand rule. It's about how the electron, when moving in a magnetic field is always forced to one particular side and not the other. When we magnify the electron, it probably looks spherical and identical from all directions. How then does the charge inside (or on) it cause it to swerve to one side always? The issue would not be as vexing to me if the electron was swerved in the direction of the magnetic field (either up or down). Because the electron looks like a perfect sphere (maybe I'm wrong on this) and is not anchored to anything, it just looks equally possible that it would go to the left or to the right but it always chooses one side. How can we intuitively explain this?

This is puzzling. How come you have a problem with electrons going one way, but not proton (or other positive charges) going the opposite way? Or what if I have a negative ion that is also "always force to one particular side and not the other"? Do you have a problem that that as well?

Zz.

 

[mmanyevere]

This is puzzling. How come you have a problem with electrons going one way, but not proton (or other positive charges) going the opposite way? Or what if I have a negative ion that is also "always force to one particular side and not the other"? Do you have a problem that that as well?

Zz.

Sure, it's just the flip side of the same question.

 

[ZapperZ]

Sure, it's just the flip side of the same question.

Then aren't you really asking on why the Lorentz force law is the way it is? This is similar to asking why gravitational force is the way it is.

Zz.

 

[mmanyevere]

Then aren't you really asking on why the Lorentz force law is the way it is? This is similar to asking why gravitational force is the way it is.

Zz.

For me it is not so hard to intuitively understand the explanation that 2 bodies of mass attract each other. Only a directly line of force is involved and it's not so hard to see how it happens. What would be difficult to understand is if gravity would force a ball rolling on the surface of the Earth from moving in a straight line. In that case how would it determine which side to force the ball? Could we come up with some design of a ball such that it would always curve to the left or right no matter how it is thrown?

 

[ZapperZ]

For me it is not so hard to intuitively understand the explanation that 2 bodies of mass attract each other. Only a directly line of force is involved and it's not so hard to see how it happens. What would be difficult to understand is if gravity would force a ball rolling on the surface of the Earth from moving in a straight line. In that case how would it determine which side to force the ball? Could we come up with some design of a ball such that it would always curve to the left or right no matter how it is thrown?

But see, what you consider to not be intuitive, it is to me.

Familiarity feeds intuition, and builds up intuition. After all, intuition has been shown to be wrong many times. Why would a helium balloon floats to the front of a train when the train is accelerating forward while the rest of us are being pushed back into our seat? Many people find that non intuitive at all UNTIL one actually learns the physics and becomes familiar with it.

Central forces do exactly the same thing. They act perpendicularly on the object that is moving in a circular path. Do you also find this non-intuitive?

Zz.

 

[mmanyevere]

But see, what you consider to not be intuitive, it is to me.

Familiarity feeds intuition, and builds up intuition. After all, intuition has been shown to be wrong many times. Why would a helium balloon floats to the front of a train when the train is accelerating forward while the rest of us are being pushed back into our seat? Many people find that non intuitive at all UNTIL one actually learns the physics and becomes familiar with it.

Central forces do exactly the same thing. They act perpendicularly on the object that is moving in a circular path. Do you also find this non-intuitive?

Zz.

This is what I'm seeking to understand beyond the answer that it is what it is. Is there some possible further explanation how electrons know to always go to the left and positrons to the right?

 

[ZapperZ]

This is what I'm seeking to understand beyond the answer that it is what it is. Is there some possible further explanation how electrons know to always go to the left and positrons to the right?

Again, do you also ask how electrons know to be attracted to a positive charge while positrons already know to go away from a positive charge?

You are really asking why these forces act the way they do, even if you think some of these are "intuitively" obvious. They are not! It is just that you are familiar with the others. But if you put them under the SAME question you're asking about the Lorentz force law, you'll find that they are equally NOT intuitive.

Zz.

 

[Khashishi]

When we magnify the electron, it probably looks spherical and identical from all directions.

Even if we regard the electron as symmetrical (ignoring spin), the magnetic field isn't.

The issue would not be as vexing to me if the electron was swerved in the direction of the magnetic field (either up or down).

If you regard the magnetic field as a 2-form (rather than a vector), then the electron does turn in the direction of the magnetic field. If you aren't familiar with two forms, the short explanation is that they are directed area elements. This is a more accurate representation of the magnetic field, but since we don't directly see the magnetic field, we usually switch to a dual representation: we represent a flat directed area element with an arrow pointing in the perpendicular direction. Mathematically, we are replacing the quantity dx^dy (which represents an area in the xy plane) with $\hat{z}$.
The magnetic field vector
$B_x \hat{x} + B_y \hat{y} + B_z \hat{z}$ is equivalent (in flat space) to the 2-form $B_x dy\wedge dz + B_y dz\wedge dx + B_z dx\wedge dy$
The sign might differ in standard literature, but don't worry about such conventions. The point is that the magnetic field turns a charge in a circle in the direction given by the magnetic field.

 

[mmanyevere]

Again, do you also ask how electrons know to be attracted to a positive charge while positrons already know to go away from a positive charge?

You are really asking why these forces act the way they do, even if you think some of these are "intuitively" obvious. They are not! It is just that you are familiar with the others. But if you put them under the SAME question you're asking about the Lorentz force law, you'll find that they are equally NOT intuitive.

Zz.

Thank you. I will read up on the Lorentz force law because so far I did not find it hard to accept the attraction or repulsion because it's along just one line of force. My problem was in understanding the force in another direction where it appears equally likely that the force could be to the left or to the right. This is where I have a hard time figuring out how the charge could always inform the particle which way to go.

 

[ZapperZ]

Thank you. I will read up on the Lorentz force law because so far I did not find it hard to accept the attraction or repulsion because it's along just one line of force. My problem was in understanding the force in another direction where it appears equally likely that the force could be to the left or to the right. This is where I have a hard time figuring out how the charge could always inform the particle which way to go.

It is neither the "charge" nor the "current" that "informs" the particle what to do. It is the FIELD.

Zz.

 

[mmanyevere]

It is neither the "charge" nor the "current" that "informs" the particle what to do. It is the FIELD.

Zz.

It's the charge being positive or negative, no?

 

[mmanyevere]

Even if we regard the electron as symmetrical (ignoring spin), the magnetic field isn't.

If you regard the magnetic field as a 2-form (rather than a vector), then the electron does turn in the direction of the magnetic field. If you aren't familiar with two forms, the short explanation is that they are directed area elements. This is a more accurate representation of the magnetic field, but since we don't directly see the magnetic field, we usually switch to a dual representation: we represent a flat directed area element with an arrow pointing in the perpendicular direction. Mathematically, we are replacing the quantity dx^dy (which represents an area in the xy plane) with $\hat{z}$.
The magnetic field vector
$B_x \hat{x} + B_y \hat{y} + B_z \hat{z}$ is equivalent (in flat space) to the 2-form $B_x dy\wedge dz + B_y dz\wedge dx + B_z dx\wedge dy$
The sign might differ in standard literature, but don't worry about such conventions. The point is that the magnetic field turns a charge in a circle in the direction given by the magnetic field.

Thanks. I will read that up

 

[ZapperZ]

It's the charge being positive or negative, no?

Yes, but a charge sitting there without the presence of any electric or magnetic field feels zero force, regardless of how much charge it has.

Zz.

 

[mmanyevere]

Yes, but a charge sitting there without the presence of any electric or magnetic field feels zero force, regardless of how much charge it has.

Zz.

If we have a charge moving at high speed in the vast emptiness of space with zero outside electric or magnetic field, can we detect a magnetic field induced by this moving charge - much like the magnetic field around a current carrying conductor? If the answer is yes then another angle to the question is how this magnetic field knows to curve in a particular direction.

 

[tech99]

If we have a charge moving at high speed in the vast emptiness of space with zero outside electric or magnetic field, can we detect a magnetic field induced by this moving charge - much like the magnetic field around a current carrying conductor? If the answer is yes then another angle to the question is how this magnetic field knows to curve in a particular direction.

To detect a magnetic field then you need something else in your empty space. For example, suppose the electron is approaching a wire carrying a current. The following paper describes how to predict its motion without resorting to magnetic fields at all. It uses the electrostatic fields and applies some simple Relativity considerations: http://physics.weber.edu/schroeder/mrr/MRRtalk.html
This removes the mystery surrounding handedness, and then you can check the result using Maxwell's Cork Screw Rule and Fleming's Left Hand Rule for Motors..
I am indebted to "jartsa" in yesterday's Classical Physics for bringing the above paper to my attention.

 

[jerromyjon]

What physical attribute of the electron causes it to experience force in one direction and not the other when it moves in a magnetic field?

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.

 

[mmanyevere]

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

That is exactly my question also. If you should ever find some interesting explanation, please share it with me.

 

[A.T.]

"Why is the force up and not down" as in this image... it logically could be either direction.

What does "logically" mean here? How does "logic" constrain it to only these two directions?

 

[jerromyjon]

How does "logic" constrain it to only these two directions?

Because from what is known about magnetism and electricity they interact at right angles.

 

[A.T.]

Because from what is known about magnetism and electricity they interact at right angles.

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?

 

[ZapperZ]

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

No, it is not "logical", because the reason why it behaves the way it is IS due to "logic", i.e. mathematics.

The reason why I haven't offered more explanation here is because the question is being asked at a very elementary level. I suspected that the OP has NOT done (i) vector calculus and (ii) has not seen the full Maxwell Equation. I did NOT want to try and inject on the fact that the "curl of the electric field" corresponds to "the time rate of change of the magnetic field, or that the "curl of the magnetic field" corresponds to "the time rate of change of the electric field". Would that have accomplished anything?

A "charge" only responds to "electric field". A magnetic field affects "magnets", or something with magnetic moment. This is where Maxwell equations (or specifically Faraday's law and Ampere's law) kick in, in which the changing or moving magnetic field corresponds to being an electric field. So the moving charge doesn't actually see a magnetic field, but rather, it sees the magnetic field being transformed into an electric field. This electric field is what acts on the charge!

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. The mathematics of classical field and Maxwell equations dictates this description.

What you guys are seeing are the consequences of these description, i.e. that left-hand or right-hand rules are the outcome of a more fundamental description of classical EM fields. 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".

Zz.

 

[mmanyevere]

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?

Back to my windmill analogy, imagine if we just discovered a windmill that we couldn't open to see its blades inside and it just looked on the outside like a perfect disk. If you blow a wind at it from the "front" it rotates clockwise and vice versa if you reversed the wind direction. Wouldn't it be legitimate to wonder why a wind perpendicular to the disk causes it to turn in one direction and not the other? Because both outcomes would look equally likely.

 

[A.T.]

Back to my windmill analogy, imagine if we just discovered a windmill that we couldn't open to see its blades inside and it just looked on the outside like a perfect disk. If you blow a wind at it from the "front" it rotates clockwise and vice versa if you reversed the wind direction. Wouldn't it be legitimate to wonder why a wind perpendicular to the disk causes it to turn in one direction and not the other? Because both outcomes would look equally likely.

A better analogy would be discovering two types of windmills, which turn in opposite directions in the same wind.

 

[mmanyevere]

A better analogy would be discovering two types of windmills, which turn in opposite directions in the same wind.

Even better!. Based on empirical evidence and without an understanding of what is actually happening inside, one could just assign a "positive" and "negative" charge to each type of windmill and still come up with formulas that accurately predict the behaviour based on the wind speed, density, angle of incidence, etc. If someone asks why the two windmills turn in opposite directions, they shouldn't be pointed to the empirical formulas as an explanation because somewhere in those formulas will just appear a conventional "+" or "-".

 

[A.T.]

If someone asks why the two windmills turn in opposite directions

But in that analogy, your question in this thread is rather:

Why does a negative windmill turn the way it does, and not the other way?

And the answer is:

If it would turn the other way, it would be a positve windmill, per definition.

 

[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.
View attachment 215014

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.)