The Application of Integral Transform Method in the Study of Physical Electrostatic Field

数学方法在物理学中占据着关键地位，对理论研究、现实教学以及实际应用有着重大意义。本文聚焦积分变换法在静电场问题中的应用，详细阐述其原理及过程。在点电荷静电势求解中，通过泊松方程结合傅里叶变换，得出不同位置点电荷的电势表达式，加深对静电场理论的理解；针对静电场边值问题，以接地金属槽为例，充分展现积分变换法简化计算的卓越效能，凸显其在解决静电场问题方面的独特价值以及数学方法在物理学科中的重要性，有助于相关领域研究与学习，推动电磁学理论与技术的发展。Mathematical methods play a crucial role in physics and are of great significance to theoretical research, practical teaching, and real-world applications. This paper focuses on the application of integral transformation methods in electrostatic field problems, elaborating on its principles and processes in detail. In the solution of electrostatic potential of point charges, by combining Poisson’s equation with Fourier transform, the potential expressions of point charges at different positions are obtained, deepening the understanding of electrostatic field theory. For electrostatic boundary value problems, taking the grounded metal slot as an example, the outstanding efficiency of integral transformation methods in simplifying calculations is fully demonstrated, highlighting its unique value in solving electrostatic field problems and the importance of mathematical methods in the physical discipline. This is conducive to research and learning in related fields and promotes the development of electromagnetic theory and technology.