a particle of mass m and charge q moving with velocity v in a magnetic field B. The velocity of the particle is perpendicular to the field, and the particle is moving in a circle

When a charged particle describes a circular path in a uniform magnetic field, the charged particle experiences a magnetic force towards the center of circular path, according to Fleming's left hand rule. Therefore the magnetic force and velocity (tangent to circular path) are perpendicular to each other during the circular motion. As the direction of displacement, is the direction of velocity, hence force and displacement are perpendicular to each other.

Therefore work done by magnetic force,

W=Fscos90=0