We report on the effect of variable magnetic field on temporal behavior of neutral copper (Cu I) transitions in laser-produced copper plasma at atmospheric pressure using optical emission spectroscopy. In the presence of magnetic field, the intensity of copper atomic lines at 510.5, 515.3, and 521.8 nm gets enhanced due to increase in electron-impact excitation rate. The enhancement factor of the neutral lines is different due to different electron-impact excitation rates. We observed that the Cu I profile consists of two components recorded in the absence of magnetic field and at 0.1 T. At magnetic field of 0.3 T, the appearance of third slow component at delayed time, i.e., 122, 130, and 140 ns for Cu I (521.8, 515.3, and 510.5 nm) is also observed. We demonstrate that the generation of slow component is related to electron-impact excitation of Cu I atom rather than backflow particles and instabilities at atmospheric pressure. The instabilities generated during the plasma deceleration by magnetic field can be reduced in the presence of air at atmospheric pressure which will be applicable to enhance the sensitivity of laser-induced breakdown spectroscopy. The fast component is least affected by the magnetic field due to longer magnetic diffusion time.