垂直电偶极子在球外侧电磁场的闭合解及验证

给出了理想导体球外侧垂直电偶极子激励电场的闭合解，解决了直接场的级数表达式的不连续性问题.同球外电磁场直接级数求和表达式的计算结果进行了比较.在相同的电磁模型下，利用闭合解对一种近似方法进行了验证：当垂直电偶极子以及场点在球体表面附近并且频率较低时，这两种方法的计算结果非常一致；当垂直电偶极子以及场点不在球体表面附近并且频率较高时，闭合解的计算结果逐渐出现了近似方法未出现的干涉现象.

The closed solution and verification of the electromagnetic field of a vertical dipole over the sphere

The closed solution of the electromagnetic filed of the vertical dipole over a perfect conducting sphere is introduced,the problem of discontinuity encountered in the series expression of the direct field is solved. Computation result is compared with the direct summation of the series form solutions of the electromagnetic filed over the sphere. Based on the same electromagnetic model, an approximate method is verified by the closed solution. If the vertical dipole and the observation point are near the surface of the sphere and the frequency is not too high, then the computation results of the two methods are guite the same. If the vertical dipole and the observation point are not near the surface of the sphere and the frequency is high, then the behavior of interference is gradually obtained by the closed solution but not by the approximate method.