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I read it on wikipidia that Coulomb law will work if both the charges are at rest relatively. Will there be an effect of magnetic field also?

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    $\begingroup$ In a reference frame where the two charges are moving each charge will produce a magnetic field, and instead of Coulomb you should use the (more general) lorentz force en.wikipedia.org/wiki/Lorentz_force the total force felt will remain the same though $\endgroup$
    – user83548
    Sep 28 '15 at 22:59
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if both charges are moving with same speed and have the same charge then their magnetic fields will be same and hence they will cancel each other out

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