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QUESTION: dear Professor Stephen , I have a general question about the motion of an electrons beam in vaccum between two charged electrodes. As you know the electrons crossing an electrical field move toward the positive electrode.
So work is made to modify the electron motion. At the same way this work is supposed to be extracted by the two electrodes , correct ?
But imaging the electrodes are charged with positive/negative charge in vacuum how can they loose their energy ?
In other words , physics book explain very well the work made on the electrons beam , this energy/work must be exchanged by the electrodes  ? I hope the question is clear ?

ANSWER: No, that's not quite right.  The electrodes are fixed, the work done on the electrons in the beam by the electric field goes into their kinetic energy.  The electrons will accelerate as they move towards the positive electrode.

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QUESTION: Dear Professor Stephen , sorry I do NOT understand your answer .
Put my question in this way : two charged electrodes can modified the electron beam for ever ? so energy transfer to the electron beams never stop?
if the electron beam receive energy , where this come from ?

Answer
I don't understand what you mean by forever.  Two electrodes, when charged, create an electric field. They're separated by a finite distance.  Electrons in them will accelerate towards the positive electrode because the electric field applies a force to charges in it.  The electrodes will stop accelerating when they either hit the positive electrode or their motion takes them outside of the electric field (if they had initial energy or if the positive electrode is only a mesh, perhaps).  Then all the work done on them is in their kinetic energy.  The energy comes from whatever charged the electrodes (to generate this charge difference, work must be done on the charges in the electrodes themselves).  The energy transfer to the electrons is accomplished by the field itself, as the electrons move in the field the energy of the field is altered.  There's energy in the field itself, see here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/engfie.html

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Dr. Stephen O. Nelson

Expertise

I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

Experience

I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

Education/Credentials
Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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