Moving electrons: magnetic and electric fields

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ninjadrummer8
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Ok I have a general question. Say I have a bunch of electrons moving in a line, not in a wire, but I guess it could be looked at as if it was in a wire.

This is my question: So if i picked a point outside of this line of moving electrons, would I find an electric field?

I know that there is a magnetic field for sure, and I know that if the electrons were NOT moving, that there would be an electric field. What I'm not sure of is if the magnetic field replaces the electric field or not.
 
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If you consider bunches of electrons traveling at (nearly) the speed of light in a vacuum tube (for example at the Stanford Linear Accelerator Center), the bunched structure of the electrons gives rise to electric fields. The same is true for a certain class of microwave electron tubes called klystrons.