# B Why do electrons obey Fleming's left hand rule?

1. Nov 13, 2017 at 8:57 AM

### 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.

2. Nov 13, 2017 at 9:49 AM

### BvU

Hello mmanyevere,

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.

3. Nov 13, 2017 at 10:53 AM

### mmanyevere

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.

4. Nov 13, 2017 at 10:58 AM

### 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.

5. Nov 13, 2017 at 11:25 AM

### mmanyevere

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?

6. Nov 13, 2017 at 11:43 AM

### ZapperZ

Staff Emeritus
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.

7. Nov 13, 2017 at 11:52 AM

### mmanyevere

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

8. Nov 13, 2017 at 11:55 AM

### ZapperZ

Staff Emeritus
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.

9. Nov 13, 2017 at 12:35 PM

### mmanyevere

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?

10. Nov 13, 2017 at 12:41 PM

### ZapperZ

Staff Emeritus
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.

11. Nov 13, 2017 at 12:50 PM

### mmanyevere

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?

12. Nov 13, 2017 at 12:57 PM

### ZapperZ

Staff Emeritus
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.

13. Nov 13, 2017 at 1:19 PM

### Khashishi

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.

14. Nov 13, 2017 at 1:19 PM

### mmanyevere

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.

15. Nov 13, 2017 at 1:24 PM

### ZapperZ

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

Zz.

16. Nov 13, 2017 at 1:28 PM

### mmanyevere

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

17. Nov 13, 2017 at 1:30 PM

### mmanyevere

Thanks. I will read that up

18. Nov 13, 2017 at 1:30 PM

### ZapperZ

Staff Emeritus
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.

19. Nov 13, 2017 at 2:23 PM

### mmanyevere

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.

20. Nov 13, 2017 at 3:35 PM

### tech99

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.