| 1. | The boundary value problem on the magnetic vector potential a is derived by introducing the magnetic vector potential a and using maxwell ' s equations
通过引入矢量磁位a并利用麦克斯韦方程组推出了以矢量磁位a为求解对象的边值问题。 |
| 2. | Finally , the impedance analytical expression for the solenoid coil with a finite - length ferrite core carrying time - harmonic current is obtained through the magnetic vector potential
最后由矢量磁位得到带有限长磁芯的放置式通电圆柱线圈的阻抗解析表达式。 |
| 3. | The main work is as follows : for the magnetic vector potential , the principle of calculus of variations is applied to convert the elliptical boundary value problem into
随着磁芯高度和半径的增大，线圈阻抗增量增大，当磁芯高度超过某一值时，线圈阻抗趋于稳定。 |
| 4. | Then , using the principle of superposition and integrating the delta - coils , we can obtain the expressions for the magnetic vector potential caused by the cylindrical coils carrying current
然后，应用叠加原理，并对圆环线圈进行积分，求得各场区通电圆柱线圈的矢量磁位表达式。 |
| 5. | Regarding the discrete magnetic vector potential and loop currents as the state variables , and combining the fem with the multi - loop method , a mathematical model of the synchronous machine with internal faults is set up in this paper
本文以矢量磁位和回路电流为求解变量，把电机的电磁场方程与反映绕组联接情况的电路方程联立起来同时求解，提出了同步发电机定子绕组内部故障的瞬态电磁场与多回路耦合的数学模型。 |
| 6. | And the expression of magnetic flux density b is got by making use of the relation of magnetic vector potential a and magnetic flux density b . finally , the equation of the magnetic flux lines is given by way of describing the distributing of the magnetic field
通过求解该边值问题得到了相应的矢量磁位a的解析表达式，然后利用矢量磁位a和磁感应强度召的关系求得了磁感应强度b的解析表达式。最后为了更直观地描述磁场的分布给出了相应的磁力线方程。 |
| 7. | With the development of edge finite element , the gauge problem is necessary to be solved when magnetic vector potential a . is used . tree - gauge is used in the edge element to assure the unity a . but tree - gauge will lead that the equation is not convergence , and that precision of result turn bad
随着棱边有限元( edgefiniteelement )法的发展，以矢量磁位a为求解变量时规范问题成为需要解决的一个问题。棱单元法中常采用树规范( tree - gauge )来保证a的唯一性。 |
| 8. | In chapter 3 , the mathematical modal of electromagnetic and temperature fields is presented by a complex magnetic vector potential , which is also applied to solve eddy current field in ansys software . then , the electromagnetic field analysis , thermal analysis and coupled - field analysis in ansys are introduced
第三章：介绍了ansys中引入复矢量磁位计算电磁场、涡流场的方法以及温度场求解的数学模型，简述了ansys软件中的电磁场、温度场以及耦合场分析。 |
| 9. | In this thesis , studies are made on the problem of time - harmonic electromagnetic fields excited by an arbitrary current dipole in spherical conductor . the problem is presented in eddy - current nondestructive test and geophysical prospecting . under the condition of magnetic quasi - static state , the boundary - value problem about modified magnetic vector potential is solved and the analytical solution is obtained
本论文针对涡流无损检测和地球物理勘探领域用到的球导体中时谐电流元的电磁问题做了研究，在磁准静态近似下，求解了修正磁矢量位的边值问题，获得了问题的解析解，并利用通用有限元分析软件做了数值验证。 |
| 10. | The solving steps are as follows : the field is divided into three regions by the cylindrical surface of the finite - length cylinder and the location of the delta - coils . because " the surface current source is placed at the interface , the non - homogenous restricted equation on the magnetic vector potential is transformed into the homogenous helmholtz equation . by using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants , the expressions for the magnetic vector potential of the three regions are solved out
在求解过程中，假定放置式圆柱线圈是由无穷多个对称圆环线圈密饶而成，首先求解含有有限长磁芯的通电对称圆环线圈的电磁场：以有限长圆柱磁芯的侧面和圆环线圈所在圆柱面为分界面将场域划分为三个小区域，由于场源放置在内边界面上，使得关于矢量磁位的非齐次约束方程转化成齐次亥姆霍兹方程，利用分离变量法求解，根据分界面郑州大学硕十研究生毕业论文摘要条件以及无限远条件确定待定常数，从而得到各场区矢量磁位的表达式。 |
