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The magnetic force depends on vecv which...

The magnetic force depends on `vecv` which depends on the inertial frame of reference. Does then the magnetic force differ from inertial frame to frame? Is it reasonable that the net acceleration has a different value in different frames of reference?

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Yes, the magnetic force differ from inertial frame to frame. The magnetic force is frame dependent.
The net acceleration which comes into existing out of this is howeer, frame independent (non-relativistic physis) for inertial frames.
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