This is my first time asking a question on this forum so I hope my question wouldn't violate any policies. Thank you in advanced for your help.

I have been trying to learn about the vacuum-tube diodes and there is a point mentioned in a lot of texts that I have not been able to understand.

In a space-charge limited condition, the cathode is heated and electrons are boiled off and leave the cathode at zero velocity. At the same time, the electric field at the cathode is zero. This is my problem. If the electric field is zero at the cathode, how could the electrons there, which have zero velocity, accelerate and move to the anode?

Thank you a lot for your help.



Good question.

The electrons have charge, and they repel each other. So the "sea of electrons" that is formed close to the cathode slowly expands - eventually the outermost electrons start to "feel" the anode and move away.

In the space charge limited case, the rate at which electrons leave the solid is limited by their internal energy and the work function of the material - there is no help from the electric field. But that doesn't mean that electrons at the edge of the cloud don't get pushed away.

  • $\begingroup$ Thank you, Floris. I guess it makes more sense to me now. Based on your answer, would I be correct if I understand that the velocities of the electrons at the cathode is actually not zero? More precisely, the first electron that leaves the cathode may have zero velocity, but the next electron would not due to the electric field created by the first electron (which is different from the electric field between cathode and anode)? $\endgroup$ – user147507 Mar 5 '17 at 1:02
  • $\begingroup$ Actually the electrons that "boil off" may have a non-zero velocity. When the "second" electron leaves the cathode it will push the "first" one away $\endgroup$ – Floris Mar 5 '17 at 2:19
  • $\begingroup$ Based on what you said, is it possible that, in fact, both electrons, the "first" and the "second", have non-zero velocities due to their electric field acting on each other? Thank you Floris. $\endgroup$ – user147507 Mar 5 '17 at 4:53
  • $\begingroup$ I suppose so. The electrons will repel each other - how much that affects their velocities depends on their relative positions. It's a bit easier to think of this once you have a lot (a "sea") of electrons ... when there is just one or two, the space charge effect isn't really in play yet and the electric field due to the anode is likely to dominate. $\endgroup$ – Floris Mar 5 '17 at 13:26

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