Magnetic fields and charged particles

[falcon32]

Hi, just reviewing some of my physics material, and realized I had a question that has never been answered for me.
I know that charged particles, traveling parallel to a magnetic field, feel no force either forwards or backwards, but feel a force perpendicular that causes them to spiral clockwise or counterclockwise, depending on the charge of the particle, in this field.

However...each charged particle has by definition its own tiny magnetic field.

Will this field interact with the larger, superimposed field? My common sense tells me that it must, as (in a macro example) I see bar magnets interacting with each other to create magnetic attraction or repulsion, respectively, between their poles.

So my question is, will the magnetic fields of the moving particles interact with the superimposed field, and what will be the direction of such a force?

The answer is probably simple but evades me for now. Thanks for helping!

 

[mfb]

If particles travel parallel to the magnetic field (lines), they travel in a straight line as no force acts on them. You need a perpendicular component to get a force.

Will this field interact with the larger, superimposed field?

Magnetic fields are linear (at least in classical physics), you can just add them to find the total field at some point. It is your choice if you call that "interaction".

and what will be the direction of such a force?

Force on what? Another particle?

 

[falcon32]

If particles travel parallel to the magnetic field (lines), they travel in a straight line as no force acts on them. You need a perpendicular component to get a force.

Magnetic fields are linear (at least in classical physics), you can just add them to find the total field at some point. It is your choice if you call that "interaction".
Force on what? Another particle?

Thanks but nevermind, I figured out my own problem. If the axis of the electron or proton was not parallel to the exterior magnetic field, the magnetic field of the particle would feel a correcting force that would swing it around to make it parallel...and once it was, there would be no more force. The field, however, would continue to rotate the particle around in a CW or CCW direction with zero net work. Correct me if I'm wrong but I think I got it. lol sometimes you just need time to think.

 

[mfb]

If the axis of the electron or proton was not parallel to the exterior magnetic field, the magnetic field of the particle would feel a correcting force that would swing it around to make it parallel...and once it was, there would be no more force.

No, it does not do this.

The field, however, would continue to rotate the particle around in a CW or CCW direction with zero net work.

There is no rotation of (elementary) particles.
No, not even spin is a rotation.

 

[falcon32]

No, it does not do this.
There is no rotation of (elementary) particles.
No, not even spin is a rotation.

Maybe I phrased this wrong for you. If two magnetic fields were at right angles to each other, would they feel mutual forces towards making them parallel? (Put two bar magnets at right angles near each other.)

 

[WannabeNewton]

For static magnetic moments, the external magnetic field will exert a torque that tries to align the magnetic moment with the direction of the magnetic field as you say. However when we have a situation where the magnetic moment is proportional to the angular momentum , there will be a precession of the magnetic moment about the axis of the magnetic field because the torque, which is the rate of change of the angular momentum, will be proportional to (in magnitude) and perpendicular to (in direction) the angular momentum.
This is the famous Larmor precession: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/larmor.html
https://en.wikipedia.org/wiki/Larmor_precession

So what you speak of will not happen for the system you are describing.

 

[falcon32]

For static magnetic moments, the external magnetic field will exert a torque that tries to align the magnetic moment with the direction of the magnetic field as you say. However when we have a situation where the magnetic moment is proportional to the angular momentum , there will be a precession of the magnetic moment about the axis of the magnetic field because the torque, which is the rate of change of the angular momentum, will be proportional to (in magnitude) and perpendicular to (in direction) the angular momentum.
This is the famous Larmor precession: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/larmor.html
https://en.wikipedia.org/wiki/Larmor_precession

So what you speak of will not happen for the system you are describing.

Thanks, I agree!

To quote my physics book from my course from a few years ago:

"A current-carrying loop experiences no net force in a uniform magnetic field, but it does experience a net torque. The orientation of the loop can be described conveniently by a unit vector n that is normal to the plane of the loop ... τ=NIAB sinθ ... This torque tends to twist the loop so that n is in the same direction as B."

--Tipler, Paul and Mosca, Gene. Physics for Scientists and Engineers. 6th ed. New York: W.H. Freeman and Company, 2008. p. 900

(B is the exterior magnetic field, n is the unit vector of the loop of current-carrying wire)

Since n is the unit vector normal to the loop of wire, it is also the vector in the direction of the magnetic field created by the current flowing through the wire.

According to the given equation, if there is a deviation from both of these magnetic fields being parallel, the angle of deviation being θ, a net torque...let me be very clear, a torque, not a force...is felt.

Thank you, Tipler and Mosca! But curse you for not teaching me about the Larmor Precession in your book :P

 

[falcon32]

No, it does not do this.
There is no rotation of (elementary) particles.
No, not even spin is a rotation.

All charged particles spiral in a clockwise or counter-clockwise direction, when in the presence of an external magnetic field. This was one of the first things I was taught, and is the fundamental principle of mass spectrometers. You must have not understood my question.

 

[physwizard]

Maybe I phrased this wrong for you. If two magnetic fields were at right angles to each other, would they feel mutual forces towards making them parallel? (Put two bar magnets at right angles near each other.)

I think you are confusing magnetic moments with magnetic fields.

 

[physwizard]

Force on what? Another particle?

Perhaps he is referring to the electromagnetic 'self-force' and whether magnetic fields play a role in it.

 

[falcon32]

I think you are confusing magnetic moments with magnetic fields.

Well this is what I'm guessing...its a known fact that charged particles undergo spiraling patterns (if they were originally moving in a straight line) or simply circular patterns (if they were holding still) when they are in the presence of a uniform magnetic field. No one disputes this, like I said, mass spectrometers are built on the principle.
So then: we fire our electron/proton into such a field, and naturally it spirals. But this means a charge is moving in an orbital fashion, right? Would that circular motion of a charged particle constitute a current, giving rise to a magnetic field? Would that field interact with the external field?
I'm just musing, physwizard, not out to say or prove anything, only doing thought experiments. Cheers.

 

[physwizard]

Well this is what I'm guessing...its a known fact that charged particles undergo spiraling patterns (if they were originally moving in a straight line) or simply circular patterns (if they were holding still) when they are in the presence of a uniform magnetic field. No one disputes this, like I said, mass spectrometers are built on the principle.
So then: we fire our electron/proton into such a field, and naturally it spirals. But this means a charge is moving in an orbital fashion, right? Would that circular motion of a charged particle constitute a current, giving rise to a magnetic field? Would that field interact with the external field?
I'm just musing, physwizard, not out to say or prove anything, only doing thought experiments. Cheers.

Hi,
Fields don't interact with fields, fields only interact with charged particles. Yes the moving charge would have a magnetic field of its own as well as an electric field of its own. These fields would not interact with the external field but rather would interact with whatever is causing that external field, for eg. if the external field is being caused by a current, then that current carrying conductor would experience a force. In addition, the fields produced by this moving charge would interact with the charge itself. This gives rise to what is known as the radiation reaction force, or self-force. This force would cause the charge to spiral inwards and emit energy in the form of electromagnetic waves.

 

[mfb]

All charged particles spiral in a clockwise or counter-clockwise direction, when in the presence of an external magnetic field.

Only if they have a velocity component perpendicular to the field. A charge at rest will stay at rest, and a charge moving parallel to the magnetic field lines will move in a straight line (assuming a uniform field).

and is the fundamental principle of mass spectrometers.

In mass spectrometers, particles are accelerated to have such a perpendicular velocity component.

You must have not understood my question.

I am quite sure that I did.

See physwizard's post for more details.

 

[falcon32]

Only if they have a velocity component perpendicular to the field.

I agree...

A charge at rest will stay at rest, and a charge moving parallel to the magnetic field lines will move in a straight line (assuming a uniform field).

Again nothing I disagree with.

I am quite sure that I did.

I'm quite sure that you did not, since you were very clear in your point about particles not rotating...something I agree with, and my point was spiral or circular motion when perpendicular to a field, not physical rotation of the particle. I blame myself for causing the confusion by using the wrong terminology in the original question.

See physwizard's post for more details.

It is an excellent post.

 

[falcon32]

Hi,
Fields don't interact with fields, fields only interact with charged particles. Yes the moving charge would have a magnetic field of its own as well as an electric field of its own. These fields would not interact with the external field but rather would interact with whatever is causing that external field, for eg. if the external field is being caused by a current, then that current carrying conductor would experience a force. In addition, the fields produced by this moving charge would interact with the charge itself. This gives rise to what is known as the radiation reaction force, or self-force. This force would cause the charge to spiral inwards and emit energy in the form of electromagnetic waves.

Hello, thanks for your very informative post! I do have one more question that I think wasn't answered -- I think, if I understand the current description of the electron, that it has an inherent property called spin. This is nothing like what we normally think of, as in the spinning of a classical sphere around an axis of rotation (since then the electron would need to be spinning with an angular velocity far greater than the speed of light, which is impossible), but nevertheless, can give rise to a magnetic moment.
(http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html)

So since we know that electrons have an inherent magnetic moment associated with the quantum property of spin, does this mean that stationary electrons have a very, very tiny magnetic field arising from such a property?