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A charged particle moving parallel to a current carrying wire with some constant velocity. Now the frame of reference is also moving with same constant velocity as that of the particle. In my book it's written that the particle would move towards the current carrying wire in same way when a stationary frame of reference is considered. But in the moving frame of reference there is no magnetic force acting on the particle, which is the cause of movement of the charged particle in the fixed frame of reference. And since the wire is electrically neutral electric force can't be in play here. So what causes the movement of the particle? And how? And if it's written wrong in my book then what's correct?

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This is a consequence due to special relativity and length contraction so causing the charge densities for the attractive or repulsive forces. Please watch this video it answers your questions.

Special Relativity and Magnetism

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