(a) Given the formula, F=qv⃗ ×B⃗ =qvBsinθF=qv→×B→=qvBsinθ, the magnetic force on a moving charged particle is always perpendicular to the magnetic field. It therefore follows that the trajectory of a moving charge is also always perpendicular to the magnetic field lines.   (b) The magnetic force acting on a charged particle can never do work because at every instant the force is perpendicular to the velocity.

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.