近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上

的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数，其代表矢量场的整体性质: 当经历连续变换时，矢量场的

局部数值发生改变但整体积分值即陈数仍保持不变; 若陈数发生改变，则表明矢量场变换的连续性条件发生破坏，矢量场出

现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上，并给出了第一陈数的直观几何意义.理论和数值结

果揭示了安培环路定理的拓扑学本质，表明拓扑概念在经典物理学中也会有广泛应用.

Topology has been widely discussed in quantum mechanics in recent years. In this paper，the integral

formula of Ampère s circuital law is re-expressed as the integral formula of the first Chern number of a vector

field defined on the torus parametric surface. The numerical simulation shows that the integral value is an integer，i.

e.，the first Chen number，which represents the global property of vector field: When the vector field undergoes

continuous transformation，the local value of the vector field changes，however the integral value，i.e.，the Chern

number，remains unchanged; if the Chern number changes，it implies the vector field has experienced a discontinuous

change and there rises the singularity in the distribution of vector field. Furthermore，the vector field is

mapped from torus parametric surface to the unit sphere by Gauss mapping，and the intuitive geometric meaning of

the first Chern number is given. The theoretical and numerical results reveal the topological nature of Ampère s circuital

law，and show that the concept of topology can also be widely applied in classical physics.