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If two electrons are travelling side by side with the same velocity with respect to me, they are standing still with respect to each other. For me, they will exert on each other an electrostatic force minus a magnetic Lorentz force. But, as seen from their point of view there is only an electrostatic force. So according to me their acceleration will be greater than the one they will "feel". So how can one solve this issue ? Maybe though the acceleration will be weaker as seen by me, the time lenght during which they will accelerate will be longer too (according to me). As seen by the electrons, the acceleration will be greater but will last shorter. Is this reasoning correct ? Can someone do the exact calculation ?

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    $\begingroup$ Transform the pure electrostatic force in their frame to the (electric,magnetic) force in your frame. What is the difference? $\endgroup$
    – Jon Custer
    Jan 16 '19 at 0:19
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    $\begingroup$ This is a standard homework problem. $\endgroup$
    – G. Smith
    Jan 16 '19 at 0:40
  • $\begingroup$ Use the fact that $E^2-c^2B^2$ is invariant, and that E-fields are squished (increased by $\gamma$) by boosts. $\endgroup$
    – JEB
    Jan 16 '19 at 1:13