A particle of mass \(m\) and positive charge \(q\) moves in a cyclotron accelerator within a uniform magnetic field of magnitude \(B\) directed perpendicular to its plane of motion. The particle accelerates twice per revolution across a gap between two semi-circular dees driven by an alternating potential difference of magnitude \(\Delta V\). Assuming that the kinetic energy increases continuously over time, which of the following expressions represents the rate of change of the particle's orbital radius with respect to time, \(\dfrac{dr}{dt}\), as a function of its instantaneous orbital radius \(r\)?