The importance of analytic solutions for verification: application to the secondary magnetic flux of a conductive disk

摘要

The method and value of analytical methods and the importance of analytic solutions for verification must be emphasised to both under- and post-graduate students. So, they must be able to: (ⅰ) derive by their own expressions for the quantities of interest, and (ⅱ) test their numerical results by an independent method. Hence, they must be motivated to try to solve any problem analytically, before proceeding to a numerical solution. Towards this aim, a sample problem is proposed and an analytic expression is derived for the secondary magnetic flux induced in a conductive disk by a time-varying magnetic field. This expression, involving elliptic and improper integrals, is finally reduced into a single integral, depending on the current distribution on the disk. Next, an analytical solution for a simplified version of the problem is obtained, which may be used for verification of the numerical solution of the more complex and general problem.