中文摘要：

索末菲积分公式可用于分析电偶极子在分层媒质中产生的电磁场问题。为了研究不同坐标系下的索末菲积分公式对电磁场表达式的影响，通过坐标系的平移和旋转得到了无限大空间中电偶极子磁矢位在不同圆柱坐标系下的表达式，利用贝塞尔函数和指数函数的积分公式将磁矢位的表达式从圆柱坐标系转化到直角坐标系，在这两种坐标系q-讨论了坐标系的旋转角度与磁矢位表达式的关系。通过数值算例对理论分析进行了验证。

英文摘要：

The Sommerfeld integral formula is used to solve the electromagnetic fields produced by the electric dipole in the multilayered media. In order to study the effect of the Sommerfeld integral formula in different coordinate systems on the analytical solutions of the electromagnetic fields, the magnetic vector potential of an electric dipole in an infinite space in different cylindrical coordinate systems is derived via the translation and rotation of coordinate system. Then the expression of the magnetic vector potential is transformed from the cylindrical coordinate systeminto the Cartesian coordinate system by the integral formulas of Bessel function and exponential function. Subse- quently the relationship between the expressions of the magnetic vector potential and the rotation angles of the coor- dinates are discussed. Furthermore, the numerical examples are provided to demonstrate this conclusion. The analyses in this paper are expected to be helpful to uncover the underlying mathematical meaning of the Sommerfeld integral formula and to calculate the electromagnetic field produced by the transmission line above the ground.