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I have read these questions:

Can an attractive magnetic force ever slow down an electron?

How does a free electron look like?

Are free electrons truly free?

Why are free electrons always moving?

Where do free electrons come from?

And it made me curious.

Now let's imagine in vacuum, in gravity free space, we have a metal box (square cube symmetrical) at rest (at least not accelerating), so that the metal box's sides are all electromagnetically repelling.

Let's say there we could place a free electron inside the box, and so the electron would be repelled by all sides of the box. Let's say the sides carry all the same charge.

In this case, would the electron ever be able to slow down inside the box because all sides are repelling it? Every time the electron tries to move close to a side, it will push it back towards inside.

Will this mechanism with time slow the electron down, when all the forces equal out and the electron will find rest at the center of the box? Since the box is symmetrical, there should be a center point where the net charge is 0.

Question:

  1. Will the electron ever find equilibrium at the center point and slow down there enough to stay at rest? Has an experiment ever been done to try to slow down an electron?
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  • $\begingroup$ I think the answer should be yes to your first question as the forces from the metal box would create a harmonic potential type valley at the centre or a stable point and cause a moving electron to oscillate about the centre thereby causing acceleration which would make it radiate EM waves hence slowing it down ultimately to the centre point $\endgroup$
    – ravjotsk
    Commented Jun 22, 2018 at 17:51
  • $\begingroup$ @ravjotsk, the electric field inside a conductor (e.g., the "metal box") is zero everywhere. physicsclassroom.com/class/estatics/Lesson-4/…. The walls of the box will not repel the electron. $\endgroup$
    – Solomon Slow
    Commented Jun 22, 2018 at 18:16
  • $\begingroup$ @jameslarge my bad. I forgot for a while that it was a metal box and thought it was just a charged box $\endgroup$
    – ravjotsk
    Commented Jun 22, 2018 at 22:00

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What you're describing is a stable equilibrium in an electrostatic field in vacuum, and that is known to be provably impossible, because of Earnshaw's theorem, which precludes exactly that condition. It is possible to 'cheat' the Earnshaw theorem by using oscillating fields that change too fast for the electron to have time to stray - this is how ion traps work - but you cannot do it with static fields.

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  • $\begingroup$ Thank you, do you think the ion trap could trap an electron this way? $\endgroup$
    – Árpád Szendrei
    Commented Jun 22, 2018 at 23:09
  • $\begingroup$ Yes, there's nothing fundamentally different from an electron to an ion; the mass is different so the trap frequencies might need to be adjusted but that's all that's needed. Most traps work with atomic ions, but as I recall there have been multiple experiments based on electron traps. $\endgroup$
    – Emilio Pisanty
    Commented Jun 23, 2018 at 0:41

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