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$\begingroup$ I would add that in second frame the moving charge is also creating electric field, not only magnetic. In fact electric field it creates actualy increases a little bit. But magnetic field is also created which counters it. At the speed of light, the magnetic force on other particle would be as strong as electric force. But in opposite direction. $\endgroup$
– MaDrung
Commented Feb 13, 2017 at 15:26

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