本文对梯度磁场下单个电子运动的轨迹方程进行了理论推导，并用MATLAB数值求解外电场为零时梯度磁场下单个电子的运动方程,得出了在梯度磁场下单个电子长时间平均位移是沿着磁场为零的线运动的结论。在此基础上，加上一个与电子平均运动方向相反的匀强电场,得出了其类似于匀减速直线运动的特性。再将情况进一步推广到随机磁场的情况，得出仅在随机磁场作用下，电子仍然沿着磁场强度等于零的线运动的结论。

In this paper, we present both analytical and numerical analysis the trajectory which one single electron covers in gradient magnetic field without electric field. The numerical solution with MATLAB shows that the average displacement of the single electron varies along the curve where .Furthermore, we added a uniform electric field which opposite the direction of the electron’s average movement, the numerical answers shows some similar character to uniformly decelerated rectilinear motion . In the situation of random magnetic field only, we still get the conclusion that the single electron moves along the curve where on average.