"电动力学"中的矢量及矢量微分运算浅析

物理学专业四大力学中,相对而言常有学生反映学习《电动力学》面临的难度明显大一些.本文根据教学经历对此作一个粗浅的分析,表明难点就在于是否使初学者充分认识矢量及其矢量微分运算的特殊基础地位.因为“电动力学”要同时研究电磁系统的时间演化和空间局域作用,所以从基本方程的形式到方程的求解,从恒定场到电磁场辐射,各部分内容无一能够离开矢量及其矢量微分运算,因而物理规律的表达形式和相关的数学运算过程都相对比较复杂.只有充分理解矢量本身的定义,熟悉对它的矢量微分运算,才能合理表达和深刻理解各部分物理定律及其应用.

Analysis of vectors and their vector derivatives in Electrodynamics

Of all four courses of mechanics,Electrodynamics is thought to be relatively more difficult to learn than others by many students.Depending on my own teaching experience,I make a rough analysis about it.It is shown that the difficulty lies in whether learners realize the fundamental role of vectors and their vector derivative operations.Since Electrodynamics treats both the time evolutions and the local interactions in the electromagnetic systems,any part of the course is based on the vectors and their vector derivative operations.Therefore both the physical law expressions and the related mathematical calculations are relatively complicated.Only when the learners understand the definitions of the vectors and are good at their vector derivative operations will they express the physical laws in a reasonable way and understand their applications.