We use the laser tweezers to create isolated pairs of topological point defects in a form of radial and hyperbolic hedgehogs, located close and attracted to a thin fiber with perpendicular surface orientation of nematic liquid crystal molecules in a thin planar nematic cell. We study the time evolution of the interaction between the two monopoles by monitoring their movement and reconstructing their trajectories and velocities. We find that there is a crossover in the pair interaction force between the radial and hyperbolic hedgehog. At small separation d, the elastic force between the opposite monopoles results in an increase of the attractive force with respect to the far field, and their relative velocity v scales as a v(d)∝d^{-2±0.2} power law. At large separations, the two oppositely charged monopoles can either attract or repel with constant interaction force. We explain this strange far-field behavior by the experimental inaccuracy in setting the fiber exactly perpendicular to the cell director.