According to Lorentz force equation a charge moving in our frame experiences magnetic force but from the frame of reference of the charge it experiences only electric force. I have heard that magnetic phenomenon are due to special relativity but did not get it clearly. Can you help?


If you have two (say) positive free charges that start at rest, they will drift apart due to Coulomb repulsion. You can (if you want) measure the force between them by timing how long it takes them to travel a distance $s$ and then using $s={1 \over 2} a t^2$ and $F=ma$

Relativity says if you do this in a moving railway carriage with the charges separated transversely to the carriage, an observer on the platform will perceive the time taken as being longer but the distance the same, and so they will perceive the force to be smaller than what you say it is.

We explain this apparent violation of Coulomb's Law by saying that there are extra forces between moving charges. The observer on the platform sees two positive charges moving side by side, and calls them 'electric currents', which attract each other due to something called magnetism, so the net force is reduced.

So time dilation slows acceleration and reduces electric forces, and we call his magnetism. Actually showing how this works mathematically is quite complicated and I'd leave it for a bit, but the concept is simple.


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