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Deviation of compass in another frame.

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Consider an inertial frame where an electric current is flowing in upward direction, a magnetic field is created and its direction is determined by the right hand rule.
In the frame of reference of the electric charges which they are at rest, how can the observer in that frame explains the magnetic field that developed in another frame moving relative to his frame? For example, how can he explain a deviation of a compass in the other frame that is moving relative to him?

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