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We have calculated in a closed form solution, in terms of modified Bessel function the first kind of order 0 and 1, for the motion of a positively charged particle in the magnetic field of an infinitely long, current-carrying wire in the nonrelativistic range. The orbits are not closed but exhibit a drift in the direction of the current with a speed that is independent of the launch angle. We found the drift velocity, drift displacement and the corresponding time, which we call the period. Keywords: Trajectory of a charged particle in magnetic field, Drift velocity, Drift displacement, Modified bessel function