Electron Deflection in Magnetic Fields: Why 90 Degrees?

[gonegahgah]

When an electron is sent passed a magnetic pole, why is the electron attracted to a place 90 degrees to its motion of travel and 90 degrees to the direction of the magnetic force causing it to deflect towards the 90 degrees to both (ie the 3rd axis)?
Why is it not attracted to the direction of the magnet?

I know the electron effects a magnetic field while it moves relative but wouldn't the attraction logically still be in the direct direction? Why isn't it?

Also, if an electron is just placed above a magnetic pole so that it has no horizontal movement what will it do then?

 

[Bob S]

The force on a moving electron with a velocity v in a magnetic field B is given by the Lorentz force law:

F = q(E + V x B)

where v x B is a vector cross product. The force is perpendicular to the plane of v and B.

Bob S

 

[gonegahgah]

That sounds like it would be right. Thx Bob.
Why is it so though?
What happens to the stationary electron which doesn't combine to form a plane?

 

[Bob S]

That sounds like it would be right. Thx Bob.
Why is it so though?
What happens to the stationary electron which doesn't combine to form a plane?

There is no force on a stationary electron by a magnetic field.
Bob S

 

[jtbell]

What happens to the stationary electron which doesn't combine to form a plane?

Huh?

 

[gonegahgah]

lol, sounds like I'm talking aeroplane electrons...

kool. The electron remains suspended except for gravity and other particle interaction I would guess. That gets me wondering how they accelerate an electron if when stationary it is non-responsive to magnetic fields; I just suddenly realize? I'm not contradicting; just realising that there must be something else you could hopefully clarify for me.

Still curious also how the electron deviates towards the third axis that is perpendicular to both its path and the source of the force rather then towards or away from the source of the force?

 

[Bob S]

That gets me wondering how they accelerate an electron if when stationary it is non-responsive to magnetic fields; I just suddenly realize? I'm not contradicting; just realising that there must be something else you could hopefully clarify for me.?

The Faraday Law of induction produces an E field around a loop through which the magnetic field is changing. Betatrons use this to get over 300 miilion electron volts. See
http://en.wikipedia.org/wiki/Betatron

Still curious also how the electron deviates towards the third axis that is perpendicular to both its path and the source of the force rather then towards or away from the source of the force?

The derivation of the Lorentz force is not straight forward. See
http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/ParticleMagneticField.htm
Another way is to do a Lorentz transform from a reference frame where the electron is at rest.

Bob S

 

[gonegahgah]

So for the first one they keep cycling a magnetic field?
Does this generate a secondary electric field of its own in the chamber or does it just effect the injected electrons making them the electric field?

Cool. The math says what is measured to happen doesn't it? Is there theory on the mechanics (the why)?

 

[Bob S]

So for the first one they keep cycling a magnetic field?
Does this generate a secondary electric field of its own in the chamber or does it just effect the injected electrons making them the electric field?

Review theory of betatron. The electrons are constantly being accelerated by the Faraday induction field as long as dB/dt > 0. Electrons radiate (synchrotoron radiation), so they are constantly radiating (losing) energy.

Cool. The math says what is measured to happen doesn't it? Is there theory on the mechanics (the why)?

The math behind the Lorentz force is firm, but not easy. In fact, Faraday first demonstrated the Lorentz force over 150 years ago. See
http://www.sparkmuseum.com/MOTORS.HTM
Bob S

 

[Bob_for_short]

...Why is it so though?...

The form of magnetic field action is an experimental fact. It is a nature feature. Our equations, if we are clever enough, take this fact into account.

 

[gonegahgah]

For the electron to be induced doesn't it have to be attracted to a magnetic force in the first place whether it is stationary or not?

 

[Bob S]

For the electron to be induced doesn't it have to be attracted to a magnetic force in the first place whether it is stationary or not?

A static magnetic field will not attract an electron. A static magnetic field cannot accelerate an electron.

Bob S

 

[gonegahgah]

Bob, I agree that a static magnetic field will not accelerate an electron.
But doesn't there have to be some static attraction so for that the movement of the magnetic field to cause the immediate electrons to follow it?
Isn't it just in a state of balanced attraction while stationary?

 

[Phrak]

You asked in a physics folder called "Classical Physics", but this very odd behavior, where things happening in perpendicular directions, disappears with the http://en.wikipedia.org/wiki/Dirac_equation" .

The electron is treated as a wave whos phase is subject to what is called the electromagnetic potential.

 

[gonegahgah]

If you have an apple on a table then the table prevents the apple from reaching the ground but the apple has weight so it is still trying to get to the ground.
So an attraction is still there.

 

[Bob S]

Bob, I agree that a static magnetic field will not accelerate an electron.
But doesn't there have to be some static attraction so for that the movement of the magnetic field to cause the immediate electrons to follow it?
Isn't it just in a state of balanced attraction while stationary?

A stationary electron is not attracted by a magnetic field. A moving electron will be deflected (but not attracted) by a magnetic field, in a direction perpendicular to its velocity. This is the way the horizontal deflection circuit (flyback coil) works in many cathode ray tube (CRT) television tubes.

 

[gonegahgah]

I trust your word Bob so I accept that what you say is the scientific position.
I must admit I find it challenging to believe that it is possible to affect anything without some form of attraction or repel but I'll have to live with it I guess.

At the macroscopic level I could have a free moving ring of ball bearings.
If I point a common tree stick at it nothing will happen.
If I wave or move the stick at or around it nothing will happen still; unless I made contact.
The ball bearings are just not attracted to the stick.
However it is different if I move a magnet over the ball bearings.
If I point a magnet at one part of the ring nothing will happen.
However, if I move the magnet above the ring in a circular motion following the ring I will induce movement of the ball bearings in the same direction.

So at the macro level we require some form of attraction to induce movement.
This is why I admit I am surprised that there is no attraction required at the nanoscopic level to induce movement of electrons.
Must be one of those things where things don't happen at the quantum level the same way they do at our level, hey?

 

[Bob S]

.
However, if I move the magnet above the ring in a circular motion following the ring I will induce movement of the ball bearings in the same direction.

What you are describing here is conceptually similar to a polyphase induction motor. The stator coils produce a rotating magnetic field that induces currents in the copper rotor squirrel cage until the rotor reaches the synchronous frequency of the stator field.
[Added] There are also variable (slotted rotor) reluctance synchronous motors that have laminated rotors with axial slots running along the outside surface. These rotors speed up until they phase lock with the stator's rotating field.

Bob S

 

[gonegahgah]

By sheer co-incidence I read the following in the book "Quantum" by Manjit Kumar:

"In classical physics, angular momentum, everyday spin, can point in any direction. What Uhlenbeck was proposing was quantum spin - 'two valued spin', spin 'up' or spin 'down'. He pictured these two possible spin states as an electron spinning either clockwise or anticlockwise about a vertical axis as it orbits the atomic nucleus. As it did so, the electron would generate its own magnetic field and act like a subatomic bar magnet. The electron can line up either in the same direction or the opposite direction as an external magnetic field. Initially it was believed that any allowed electron orbit could accommodate a pair of electrons provided that one had spin 'up' and the other had spin 'down'. However these two spin directions have very similar but not identical energies, resulting in the two slightly different energy levels that gave rise to the alkali double lines - two closely spaced lines in the spectra instead of one."

Does the reference to magnetic fields bear any relevance to what we are discussing or is it an idea that was later supplanted - I haven't finished the book yet; the book does seem to be about the evolution of our understanding?

 

[Bob S]

Does the reference to magnetic fields bear any relevance to what we are discussing or is it an idea that was later supplanted - I haven't finished the book yet; the book does seem to be about the evolution of our understanding?

No relevance. Learn about electric motors. If you are interested in permanent magnet rotors in electric motors, read about brushless permanent magnet dc (BLDC) motors in
http://oretano.iele-ab.uclm.es/~mhidalgo/temas/Brushless/00885a_fundamentos_BLDC.pdf
I think you should learn a little electrical engineering before you complete your education in quantum mechanics.
Bob S