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Does the rotation of Earth make two electrostaticaly charged bodies fixed on its surface interact magnetically (with each other)? If yes, is this interaction different as geographical latitude changes?

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Not if you're observing them from their own rest frame - that is, you're near them and also comoving with Earth's surface. An observer in the charge's rest frame measures an electric field and no magnetic field, and measures the charges moving as predicted by Coulomb's law. An observer moving relative to the charges measures an electric field and a magnetic field, and measures the charges moving as predicted Lorentz' law.

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