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Let's imagine a stretched spring with a negative Q charge at each end. At equilibrium, the repulsive electrostatic force and the force exerted by the spring on the charges cancel each other. If we increase or decrease one of the charges, the length L of the spring will change, and this will make a bell ring. Now I suddenly run in a direction perpendicular to the spring. In my reference frame, a tiny attractive magnetic force will appear. The spring will shorten and the bell will ring. Is this correct ? I know similar questions on the relativistic effect etc. have been posted, and I have read many, but it seems to me none answers my question.

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The general rule is that whenever you change reference frames, $\textit{both}$ electric and magnetic fields transform exactly the way to prevent the paradoxes of the type you have described.

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  • $\begingroup$ OK so does this mean that the force the charges exert on each other remains the same (= to the force exerted by the spring ) ? Which means that the electrostatic force increases by an amount equal to the magnetic force ? $\endgroup$
    – Anarchasis
    Oct 17, 2022 at 21:24

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