# How to confine electric charges

1. Jan 14, 2010

### Gerenuk

What sort of field do you need to confine electric charges?
Is an electric field alone possible?
Do the charges have to circle or can they be stationary?

What parameters are important for this to work.

2. Jan 14, 2010

### Bob S

A central electric field can confine electric charges without circular motion. A single proton will confine a single electron in a bound state without orbital angular momentum (i.e., not in a "circle"). A helium nucleus will confine two. A magnetic bottle will simultaneously confine moving charges of both polarities in helical orbits. See
http://en.wikipedia.org/wiki/Magnetic_mirror
Bob S

[added] Actually, a single proton can confine two electrons. The binding energy of the "valence" electron is only about 0.75 eV, and can be detached with an IR laser (wavelength < ~10,000 Angstroms). H-minus ions are often used as a source of protons in proton accelerators.

Last edited: Jan 14, 2010
3. Jan 14, 2010

### Gerenuk

I'd like to confine lots of protons. Do you mean I need a strong negatively charged wire?

Which other possibilites do you have?
Can I set up a magnet mirror to confine a bunch of protons in a limited space?

4. Jan 14, 2010

### Bob S

No.
The magnetic bottle can confine orbiting charged particles of either polarity. See
http://en.wikipedia.org/wiki/Magnetic_mirror
Solenoidal magnetic fields with magnetic "caps" on the ends have been used to do precision elementary particle physics experiments. The magnetic "caps' confine the charged particles axially-confined helical orbits.
Bob S

5. Jan 14, 2010

### Gerenuk

Just to make sure: there is no sensible way to do this with electrostatic fields alone?

Do I need to set up a particular motion of the charges in order to confine them in an magnetic bottle?

(I mean just putting in a bunch of protons won't work... in all directions?!)

There is no way to confine a bunch of protons with random directions?

6. Jan 14, 2010

### Bob S

The Penning trap uses a solenoidal magnetic field combiled with electrostatic fields to confine particles axially:
http://titan.triumf.ca/equipment/penning_trap/index.shtml
Here is a purely electrostatic ion beam trap
http://www.astro.columbia.edu/~savin/papers/massspec.pdf
Bob S
http://fisica.unicam.it/quele/docs/planar_trap_paper.pdf

There is a class of microwave tubes called crossed-field tubes (crossed E and B), of which the simplest is the magnetron. In this tube, elecrons emitted from a hot cathode are accelerated toward an anode, and in the process are deflected by an axial magnetic field. The result is that the electrons undergo cycloidal (~cyclotron) motion at microwave frequencies. See
http://en.wikipedia.org/wiki/Cavity_magnetron
In principle, protons could also undergo a similar motion in a cylindrical-radial electric field and an axial magnetic field. The best source for the theory of a magnetron could be found in EE textbooks.

Last edited: Jan 14, 2010
7. Jan 14, 2010

### Andy Resnick

Maybe I'm missing the point, but isn't that what a capacitor does? Likewise, a battery or electrolytic solution- say, an acid with pH <7?

8. Jan 14, 2010

### Gerenuk

I suppose if you have enough attractive charges, then the particles cannot espace. Probably when the sum of kinetic energies does not exceed the espace energy for a single particle, right?

Edit: But wait, arent the partners particles acting repulsively too. Why in fact does a capacitor not lose particles?

9. Jan 15, 2010

### GRDixon

According to "The Feynman Lectures on Physics", V2, Sect. 5-2, "There are no points of stable equilibrium in any electrostatic field --- except right on top of another charge."

10. Jan 15, 2010

### Gerenuk

I didn't realize. So when a normal particle is confined in some container with wall, it's due to quantum mechanical effects at the walls? Electrostatics cant explain why a container is sealed?

11. Jan 16, 2010

### GRDixon

My take on the Feynman quote is that the author was talking about a disconnect between the concept of "normal" particles and Maxwell's theory. In general, texts routinely posit stable distributions of charge ... spherical shells of constant radii, etc. ... but Maxwell's theory provides no explanation for how such stable distributions can persist in time. In view of the Feynman quote, when we talk about a spherical shell of charge (for example), we must implicitly assume some non-electromagnetic agent is preventing the distribution from dissipating into space. It's a nasty little assumption that's rarely mentioned in EM texts.

12. Jan 16, 2010

### fluidistic

Maybe Feynman made an allusion to Earnshaw's theorem? http://en.wikipedia.org/wiki/Earnshaw's_theorem

13. Jan 16, 2010

### Gerenuk

An idea: does the situation change if we allow for dynamics? I mean can atom cores with orbiting electrons create a stable structure?

14. Jan 16, 2010

### GRDixon

To my knowledge even classical electrodynamics can't produce such a confinement. If the particles are accelerating, they classically emit radiant energy. The confinement of electrons in atoms was of course the motivation for inventing quantum theory.

15. Jan 16, 2010

### GRDixon

In a way, yes. But my impression is that the Feynman quote refers to a continuous distribution of charge (e.g. a spherical shell of charge), whereas Earnshaw refers to multiple point charges which are themselves somehow kept from "evaporating" into space.

16. Jan 16, 2010

### Prologue

A spherical shell of charge has no effect on the stuff inside it anyway, so you don't even have to make that assumption. Remember that inside the shell, the voltage is constant, so there is no force on a particle of either charge. Therefore no confining 'in a certain place' (other than the whole shell) going on. Once a particle reached the edge of the sphere after just drifting, it would either shoot out or get sucked back in, depending on the charge. So I guess some charges will be kept in there but they aren't kept in a specific spot they will drift in the interior.

17. Jan 16, 2010

### GRDixon

I agree. The spherical shell was a poor choice. A solid sphere of charge might have been a better one. Somewhere in his texts Feynman, in the course of discussing the electric field right AT a surface charge, suggests that it's the average just "in front of" and "in back of" the sheet. In the context of the spherical shell he might have argued that the E field at a point right IN the shell is q^2/(2)(pi)(eps0)(R^2). That being the case, every increment of charge in the shell might be expected to experience an increment of outward pointing force, and we might expect the shell would expand with time (in the absence of some other, constraining, implied, non-electromagnetic, inward pointing force increments).

18. Jan 16, 2010

### Prologue

I have a problem with the average argument. Any time I have seen it, it has been in the context of a parallel plate capacitor, and the average argument just 'happens' to be correct there. The average is E/2, where E is the field inside the capacitor. This quantity is correct but there is a real reason for why that is, rather than 'it is the average'. The real reason is that the surface can't apply a force to itself in the normal direction, so the only thing that contributes to the force (therefore the field) is the other plate on the capacitor. Since the field doesn't vary with distance, it is merely half of the original E field in the capacitor (this is because the E field in the capacitor is a sum of the two fields from the plates, each plate with E/2). If you have an example that shows why the average argument is true in a general case, I would love to see it, I just can't believe that it is true without that though.

19. Jan 17, 2010

### GRDixon

Very good eye! Your capacitor example is precisely the Feynman passage I had in mind, and I remember having the same reaction as you describe upon reading it. In my opionion it's one of the few times when Feynman erred. (Perhaps he was repeating what an earlier mentor had taught.) As for another example, I haven't run across any, nor can I think of any. The thought-provoking aspect of the spherical shell is, in my mind, the infinite rate at which the magnitude of E changes as one crosses the shell. Maxwell might have suggested that point charges, line charges and sheets of charge don't exist in Nature. His equations suggest that charge is always continuously distributed in 3 dimensions. But EM texts wouldn't be nearly as intuitive and easy to grasp if it weren't for the IDEAS of point charges, etc. For example, in Chap. 28 of V2 ("Electromagnetic Mass) Feynman has a lucid discussion using the spherical shell as a base system. Fun stuff to think about! Thanks for responding.