Final answer:
The work done by a magnetic field on a charged particle when it completes one full circle is zero because the magnetic force is always perpendicular to the velocity of the particle, and thus cannot do any work.
Step-by-step explanation:
The question is about a charged particle with mass m and charge q moving with speed v in a circular path of radius r in a uniform magnetic field B. The work done by the magnetic field when the particle completes one full circle is queried. Magnetic forces do no work on a moving charge because they are always perpendicular to the direction of the velocity.
Therefore, they cannot change the speed or kinetic energy of a charged particle, but only its direction. Since work is defined as the force along the direction of displacement times the displacement, and the magnetic force is always perpendicular to the displacement, the work done by a magnetic field on a charged particle is zero.