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Magnetic Force on Electrons





Dennise
We know electrons in motion are affected by and can be controlled by magnetic fields. Cathode ray tubes use magnetic deflection to precisely control electron beams that strike a screen and render visual images. Before LCD and plasma TV's, older TV sets used this principle to produce screen images watched by millions. Strong electric fields produced by TV's high voltages propelled free electron beams toward the screen, while simultaneously a precisely controlled magnet field deflected the beams side-to-side and up-n-down to produce the screen's image.

This is a simple question ..... what about stationary electrons .... if indeed there are any? Are the positions of such 'at rest' electrons influenced by magnetic fields?
Bikerman
My understanding is that electrons cannot be stationary.
One simple way of explaining it that Feynman once gave - semi tongue in cheek - went something like this:
The uncertainty principle tells us that we can't know where it is at a precise time. The more precisely we know one the more uncertainty in the other.
If an electron stopped then we would know where it was and when it was and Heisenberg would come back to haunt us.
Smile
Mike can give you a much better explanation, but what I think I know is that it can never have zero energy and therefore it must be 'flicking around' a point, rather than stopped.
Ankhanu
Bikerman wrote:
My understanding is that electrons cannot be stationary.
This is my understanding as well... but I have not looked into this aspect of physics very deeply at all and was somewhat reluctant to say so Wink
kelseymh
Dennise wrote:
This is a simple question ..... what about stationary electrons .... if indeed there are any? Are the positions of such 'at rest' electrons influenced by magnetic fields?


As Bikerman said, there's no such thing (in our universe) as a "stationary" electron. The easiest way to explain it is by describing the actual device you would use to make stationary electrons, and how it would work.

First, you need a source of electrons. Set up a vacuum system, and put a metal filament connected to a current source in the vacuum. Run current to heat the metal (choose something like tungsten, which won't melt) and eventually it'll get hot enough that surface electrons will "evaporate" off. Connect the filament to a high voltage source, and the other end of your vacuum system to ground, and those hot electrons will stream from one end to the other (this is how old-fashioned TVs, and X-ray tubes, work).

But you want "stationary" electrons. Okay, so we need to cool off our beam. In the vacuum system, introduce a very dilute gas of atoms (like helium) at cryogenic temperatures. As the electrons pass through the gas, they will be more likely to transfer their energy to the atoms (and hence, cool down) than vice versa. If you're very clever, you can set things up with many passes back and forth, and get the electrons down to very low temperatures.

Finally, take your cold electrons, still in vacuum, and put them between plates at some voltage. With a clever system, you can box the electrons in from all directions. Once in the box, you can continue to use cooling techniques to get them really close (in principle, arbitrarily close) to absolute zero.

But what happens? Now we have to turn to quantum mechanics. With your box of plates, what you have done is confined your electron(s) in a potential well. The electrons are really cold, so they are non-relativistic. So pull out Schrodinger's equation and see what it says. It says that the potential well has discrete energy levels, and when the electrons have their minimum possible energy (i.e., their minimum possible motion, they populate those levels from the lowest one, filling them up and up, until all the electrons are accounted for.

Now, the interesting thing about those energy levels is that their spacing is inversely proportional to physical dimensions of the well. A big, flat well has closely spaced levels all very close to zero. A narrow, compact well has widely spaced levels which get to (relatively) high energy values. So the tighter you try to hold the electrons "in one place", the more energy, and hence the more "jittering" (zitterbewegung) they experience.
Dennise
kelseymh,

Wouldn't this be easier and more practical:

Place your filament at one end of a clear glass tube containing a rare gas, with a metal plate at the opposite end. Now connect an adjustable DC voltage source between the filament and the plate and heat the filament to produce free electrons. Then adjust the voltage so one can see (better in darkness) the electron path from the filament to the plate. Place a permanent magnet against the tube at a fixed position (say the tube's midpoint) and observe the path deflection.

Now reduce the voltage in steps to slow the electron's speed and again observe the path deflection with each voltage step reduction. If the electron beam deflection reduces with voltage reduction (and electron speed) then we would know the deflection is some function of electron speed. In the limit, could we expect at zero electron speed there would be zero deflection, and conclude electrons 'at rest' are not influenced by a static magnetic field?

My physics is quite rusty and the filament's work function and quantization effects may influence the above experiment is such away as to render the results inconclusive. If the voltage doesn't change the electron's speed, then of course all bets are off.

In principle, do you think this setup would work?
kelseymh
Dennise wrote:
Wouldn't this be easier and more practical:


Yes, what you describe is easier. What I was trying to do was describe how an actual trapping system works in the lab (deliberately skipping the use of magnetic fields to confine the charged particles tranversely).

Quote:
In the limit, could we expect at zero electron speed there would be zero deflection, and conclude electrons 'at rest' are not influenced by a static magnetic field?


You don't actually need to do this sort of thing to reach that conclusion. It follows from Maxwell's equations, if you ignore the fact that electrons have spin (and hence a magnetic moment). The force on a moving charge in a magnetic field is given by F = qp x B (in units where everything important is unity Smile. At p=0, the force is trivially zero.

For electrons, of course, the spin comes into play, and even at rest the magnetic field can flip the spin, changing the electron's energy.
jajarvin
Electrons are only stationary at absolute Zero or -273.15 Celsius.
Dennise
[quote="kelseymh"]
You don't actually need to do this sort of thing to reach that conclusion. It follows from Maxwell's equations, if you ignore the fact that electrons have spin (and hence a magnetic moment). The force on a moving charge in a magnetic field is given by F = qp x B (in units where everything important is unity Smile. At p=0, the force is trivially zero.

Yes, that explains it nicely.
asnani04
Stationary particles are not affected by magnetic fields. If at all electrons are found stationary (which I doubt), they won't be compelled to move by a magnetic field, be it in any direction. According to Biot Savart's Law, and various other laws of physics, the force acting on a charged particle in a magnetic field B is given by,

F = q(v x B)

That is, Force vector is equal to charge of the particle multiplied by the cross product of its velocity and Magnetic field. If the velocity is zero, the whole expression reduces to zero. Thus, no magnetic force acts on an electron kept stationary in a magnetic field.
twotrophy
Bikerman wrote:
My understanding is that electrons cannot be stationary.
One simple way of explaining it that Feynman once gave - semi tongue in cheek - went something like this:
The uncertainty principle tells us that we can't know where it is at a precise time. The more precisely we know one the more uncertainty in the other.
If an electron stopped then we would know where it was and when it was and Heisenberg would come back to haunt us.
Smile
Mike can give you a much better explanation, but what I think I know is that it can never have zero energy and therefore it must be 'flicking around' a point, rather than stopped.


Electrons orbit around neutrons and electrons at an extremely fast speed. In reality, an atom mostly consists of empty space. I hope this helps.
kelseymh
twotrophy wrote:
Electrons orbit around neutrons and electrons at an extremely fast speed.


This is a classical analogy, reminiscent of the Bohr model, and does not reflect reality. The wavefunctions of electrons in a ground-state atom are spread out through the full volume of the atom, in shapes corresponding to the orbial angular momentum of each one.

For so-called "Rydberg atoms", where the outermost electron has been promoted to an extremely highly excited state (typically n>50), the electron wavefunction can be measured as somewhat localized, and travelling around the nucleus in a circular "orbital" path.

Quote:
In reality, an atom mostly consists of empty space. I hope this helps.


This is correct. The size of the orbitals are approximately 10 nm, while the low-energy "classical radius" of the electron (that is, how big it seems to be if you hit it with something) is 3 fm. Thus, when you probe an atom with a low-energy projectile, most of the time you won't hit either the nucleus or the electrons, all of which are several orders of magnitude smaller than the atom itself.
asnani04
kelseymh: great explanation!
abhinavm24
hmmm. old school tv sets.
good to know how they worked.
lemonedia
<Oh nononono....most definitely NOT having that.
post deleted - Moderator>

A quick word to the wise, since you are new.
Your posting was not acceptable. Claims that over-unity devices live in some dark archives on the web are bull crap, not science.

You may, of course, think otherwise - as is your right,
BUT
a) You would be wrong.
a) I am the moderator.

So it really isn't up for discussion on these boards - take it somewhere else like chat. These boards are for science only.

<Bikerman>
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