长直交变电流磁场中圆线圈的感应电动势和感应电流

Induced Electromotive Force and Induced Current of a Circular Coil in Magnetic Field of a Long Direct Alternating Current

旨在计算长直交变电流在共面圆形线圈中产生的感应电动势和感应电流.利用磁场的安培环路定理、法拉第电磁感应定律等物理原理,以及残数定理、一阶线性非齐次微分方程等高等数学知识,详细推导了导线与线圈圆心之间的距离大于线圈半径时圆形线圈中产生的感应电动势和感应电流,并得到了他们的解析表达式.望本文可以为教师和同学们提供一些有用的参考,有利于同学们更好地掌握感应电动势和感应电流的求解方法以及高等数学知识的运算.

The purpose of this paper is to calculate the induced electromotive force and induced current of a circular coil in magnetic field of a long direct alternating current.By using the physical principles of Ampere circuital theorem and Faraday's law of lectromagnetic induction,and the mathematical knowledge of the residual number theorem and the first order linear non homogeneous differential equation,the induction electromotive force and induction current in the circular coil are derived in detail when the distance between the direct current and the coil center is bigger than the radius of the coil.And their analytical expressions are also obtained.We hope it can provide some useful reference for teachers and students,and can help students to better grasp the solution method of induction electromotive force and induction current and the use of higher mathematics knowledge.