A particle of mass $M$ and charge $Q$ moving with velocity $\vec{v}$ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes one full circle is:

The force acting on a charged particle in a magnetic field is given by $\vec{F}=Q(\vec{v}\times \vec{B})$. This force is always perpendicular to the velocity $\vec{v}$ of the particle.Since the force is perpendicular to the instantaneous displacement ($d\vec{s}$), the instantaneous work done is:
$$dW=\vec{F}\cdot d\vec{s}=0$$
Furthermore, for a complete circle, the net displacement is zero. Thus, the total work done by the magnetic field is zero.