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As the picture above, there is a uniform magnetic field from back to front. Put a positive charge in (x,y). Then there is an observer moving along the y-axis at a constant speed(v). Does it seem that the positive charge influenced by the Lorentz force(F=qvB) for the observer?

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There is no force in the frame of reference of your diagram. There is therefore no force on the charge in the moving frame of reference.

Whilst force is not a relativistic invariant, it is transformed by multiplicative factors. So a force of zero in one frame of reference cannot become non-zero in another.

The way that works here is the B-field must also be transformed in the moving frame (e.g. see here). The transformation results in a different B-field $\vec{B}' =\gamma \vec{B}$, where $\gamma$ is the usual Lorentz factor and an electric field, where $\vec{E}' = -\vec{v}\times \vec{B}'$, leaving the total force on the charge equal to zero according to the moving observer.

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