A charged particle moves in a uniform magnetic field with constant speed. What is the work done by the magnetic force after one complete circular revolution?
Zero
The magnetic force on a moving charge is \(\vec{F} = q(\vec{v} \times \vec{B})\), which is always perpendicular to the velocity.
Work done = \(F\,ds\cos 90^\circ = 0\) at every instant, since the force is always perpendicular to the displacement.
So the speed and kinetic energy stay constant; the field only changes the direction of motion, making the particle move in a circle.
The work cannot be positive or negative (energy would then change), and it is not equal to the kinetic energy.
Hence, the answer is Zero.
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Important Questions from Motion in a Magnetic Field
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