A particle with positive charge \(q\) and mass \(m\) enters a region of uniform magnetic field \(\vec{B}\) directed into the page with an initial velocity \(\vec{v}_0\) perpendicular to \(\vec{B}\). Inside the field, the particle travels along a circular arc of radius \(R\) and total path length \(s\). Which of the following correctly identifies the work done on the particle by the magnetic field over the path length \(s\), and provides the correct physical justification?