  The topological approach has recently been successfully employed to
investigate timelike circular orbits for massive neutral test particles. The
observed vanishing topological number implies that these timelike circular
orbits occur in pairs. However, the behavior of charged test particles in this
regard remains unexplored. To address this issue, our study focuses on
examining the influence of particle charge on the topology of timelike circular
orbits within a spherically symmetrical black hole spacetime holding a
nonvanishing radial electric field. We consider four distinct cases based on
the charges of the particle and the black hole: unlike strong charge, unlike
weak charge, like weak charge, and like strong charge. For each case, we
calculate the corresponding topological number. Our results reveal that when
the charge is large enough, the topological number takes a value of -1 instead
of 0, which differs from the neutral particle scenario. Consequently, in cases
of small charges, the timelike circular orbits appear in pairs, whereas in
cases of larger charges, an additional unstable timelike circular orbit
emerges. These findings shed light on the influence of the particle charge on
the topological properties and number of timelike circular orbits.
