关于一道感生电动势例题计算的思考

THE SOLUTION BASED ON THE CALCULATION OF AN INDUCED ELECTROMOTIVE FORCE EXAMPLE

对于感生电动势的理解和计算是学习电磁学过程中的重难点,现有电磁学教材中关于感生电动势的计算方法大多分为法拉第电磁感应定律计算法与定义法。但是在使用定义法计算时,大多教材在感生电动势例题的解题过程中,没有明确指明不同变量的矢量方向以及微分变化方向的关系。因此在求解感生电动势时,如果不留意各矢量变化关系往往会导致方向混乱、正负号有误的问题,使得出的结果与正确结果恰恰相反。本文对一道求解感生电动势的经典例题加以分析,首先用法拉第电磁感应定律的方法进行求解得到正确结果,之后在定义法的基础上提出三种可行且明晰的方法——弧度法、直接法和中点坐标原点法。采用这三种方法,可以清晰准确地判断各矢量及其变化关系,其得到的结果与法拉第电磁感应定律得到的结果一致。

In the process of learning electromagnetics, one of the difficulties is to understand and calculate induced electromotive force. In the existing textbooks, the general methods to solve the problems about induced electromotive force are using Faraday law of electromagnetic induction or the definition method. However, when using the definition method, most textbooks do not indicate the relationship about the vector direction of different variables and the direction of differential change clearly during solving examples of induced electromotive force. Therefore, in solving the induced electromotive force, if we do not pay enough attention to the relationship between the vector changes, the vector’s direction is often confused and the sign is fallible, so that the result is opposite of the correct result. In this paper, a classical example for solving the induced electromotive force is analyzed. Firstly, the method of Faraday law of electromagnetic induction is used to obtain the correct result, and then we come up with three feasible and clear methods based on the definition method. They are radian method, direct method, and midpoint coordinate origin method. Using these three methods, vectors and their variations’ relationships can be judged accurately. The results obtained by these three methods are consistent with the results obtained by Faraday’s law of electromagnetic induction.