There's a voltage difference of 1000 Volts between two points 2 meters apart. An electron starts at the point of lower potential and is left to travel alone in a straight line until it reaches the other point. What speed does the electron have when it reaches the second point?

gasavasiv

gasavasiv

Answered question

2022-10-19

There's a voltage difference of 1000 Volts between two points 2 meters apart. An electron starts at the point of lower potential and is left to travel alone in a straight line until it reaches the other point. What speed does the electron have when it reaches the second point?
Whether the retardation effects of the radiation of the electron are important here. I tried doing it using the relativistic formulae for the kinetic energy and got
v = c 1 ( m e c 2 m e c 2 + V ) 2
where m e is the electron mass, c the speed of light, V the voltage difference between the two points, and v the final speed of the electron.

Answer & Explanation

na1p1a2pafr

na1p1a2pafr

Beginner2022-10-20Added 16 answers

You need to distinguish between retardation and radiation.
Retardation usual refers to the effect of limited propogation seeds on interactions. That is we replace
a g = G M r 2
with
a g , r e t = G M r ( t r c ) 2 .
This only matters if
1. The ration of velocities in the system to propogation speeds are significant, or
2. The effect is constantly in one direction
in other cases (as in retarded Newtonian gravity in the solar system) it simply results in a constant correction to some effective parameter of the system (reduced mass in our example).
In your case, you have a static field which means that E ( t ) = E and the problem reduced to original case. There is no effect due to retardation.

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