We present a computational method to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials generated by moving point charges in arbitrary motion with varying speeds. Our method explicitly calculates the retarded time of the point charge along a discretized grid, which is then used to determine the fields and potentials. The computational approach, implemented in python, provides an intuitive understanding of the electromagnetic waves generated by moving point charges and can be used as a pedagogical tool for undergraduate and graduate-level electromagnetic theory courses. Our computer code, freely available for download, can also approximate complicated time-varying continuous charge and current densities, and can be used in conjunction with grid-based numerical modeling methods to solve real-world computational electromagnetics problems such as experiments with high-energy electron sources. We simulate and discuss several interesting example applications and lab experiments including electric and magnetic dipoles, oscillating and linear accelerating point charges, synchrotron radiation, and Bremsstrahlung.

中文翻译：

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时空计算和可视化移动点电荷产生的电磁场和电势

我们提出了一种计算方法，可以直接计算和可视化库仑，辐射和总电磁场的方向分量，以及任意速度下以任意速度移动的点电荷所产生的标量和矢量电势。我们的方法显式计算沿离散化网格的点电荷的延迟时间，然后将其用于确定场和电势。计算方法，在python中实现可以直观地了解由移动点电荷产生的电磁波，并且可以用作本科和研究生水平的电磁理论课程的教学工具。我们的计算机代码可免费下载，它也可以近似复杂的时变连续电荷和电流密度，并且可以与基于网格的数值建模方法结合使用，以解决现实世界中的计算电磁学问题，例如高能实验电子源。我们模拟并讨论了几个有趣的示例应用程序和实验室实验，包括电和磁偶极子，振荡和线性加速点电荷，同步加速器辐射和Bre致辐射。