Effect on electrostatic charge from accelerating electrons

[msat]

I'm trying to understand (well, maybe in an oversimplified way) what permanent changes, if any, would be experienced by a positive electrostatically charged plate used to accelerate a free electron in a vacuum, but where the electron would not strike the plate.

I assume there would be some sort of temporary effects on the plate due the the field interactions between the two, but then some distance after the electron passes by, the plate charge would revert to its initial state - unaffected. But how could that be, if energy must be conserved, how would it add momentum to the electron if the plate charge is able to revert back to its initial state? So therefore the charge on the plate must be permanently changed, but by what mechanism?

 

[mfb]

You have to get electrons to the source which has to be at a higher potential energy - this needs power from elsewhere. There are no changes to the positive plate.

 

[msat]

mfb,

what do you mean by "have to get electrons to the source"? Are you referring to an electron emitting cathode, or you mean having to initially put a charge on the plate?

 

[mfb]

The cathode which emits the electrons. If you don't "replenish" them (have a current flow against a potential difference), you will stop accelerating electrons quickly.

 

[msat]

The specifics of the electron source aren't particularly relevant to the question, imo, though I think it's safe to say you are correct.

Embarrassingly, it just dawned on me that the change I was seeking is simple Newtonian physics; the force imparted on the electron which altered its momentum would result in an equal and opposite force on the plate.

But leaving it at that puts a bad taste in my mouth. If we do start considering the electron source, specifically a field emission gun, and besides that and the charged plate, we also add an electron trap and put a conductor between the trap and gun, you'll have a continuous flow of current (assuming the trap catches 100% of the electrons, and there's no spontaneous emissions in the rest of the circuit). That can't be, but why?

 

[mfb]

Conservation of energy is useful only if you include all components of your system, or account for external sources/drains of energy.

But leaving it at that puts a bad taste in my mouth. If we do start considering the electron source, specifically a field emission gun, and besides that and the charged plate, we also add an electron trap and put a conductor between the trap and gun, you'll have a continuous flow of current

Without a power supply, the trap and the gun will be at the same potential quickly, at that point flow stops.

 

[msat]

Without a power supply, the trap and the gun will be at the same potential quickly, at that point flow stops.

There would be a potential between the plate and the gun, which would cause it to emit electrons and it turn be at a positive charge (not for long, of course)... In theory.

 

[mfb]

(not for long, of course)

That is the point. You have some energy stored in the system as it acts like a capacitor. You can convert that energy to kinetic energy of electrons or heat.

 

[msat]

What I mean was that the field generated by the charge imbalance would induce a current down the conductor so that as long as the other end was able to collect electrons, and the cycle would continue as the gun continued to emit electrons.

 

[mfb]

There is no cycle. You have a capacitor that discharges over time, without external power supply the system stops quickly as all electrodes reach the same potential.