Suppose a charged particle moves with a velocity v near a wire carrying an electric current. So, a magnetic force acts on it. If the same particle is seen from a frame moving with velocity v in the same direction, the charge will be found to be at rest. Will the magnetic force become zero in this frame? Will the magnetic field become zero in this frame?

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Solution

Magnetic force becomes zero as the particle is at rest in this frame of reference and we know that force on a particle,

F = qvBsin( $θ$ ), where v is the velocity of the particle.
So, when v = 0, F = 0.
Magnetic field on the particles still exists because the current is independent of the frame of reference. For any reason, if the electrons of the wire seem to be at rest in a frame of reference, the protons are still flowing opposite to the frame of reference. Due to this, the current and the magnetic fields still exist.

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