A new static and azimuthally symmetric magnetic monopolelike object, which looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the monopole position and vanishes at the origin, is discussed. This monopolelike object is inspired by an analysis of an exactly solvable model of Berrys phase in the parameter space. A salient feature of the monopolelike potential ${cal A}_{k}(r,theta)$ with a magnetic charge $e_{M}$ is that the Dirac string is naturally described by the potential ${cal A}_{k}(r,theta)$, and the origin of the Dirac string and the geometrical center of the monopole are displaced in the coordinate space. The smooth topology change from a monopole to a dipole takes place if the Dirac string, when coupled to the electron, becomes unobservable by satisfying the Dirac quantization condition. The electric charge is then quantized even if the monopole changes to a dipole near the origin. In the transitional region from a monopole to a dipole, a half-monopole with a magnetic charge $e_{M}/2$ appears.
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