Analytical solution for transient, diffusing fields inside a ring conductor with rectangular cross-section is discussed. Some details from the paper by V. Thiagarajan with additional clarifications are presented. The comment paper on the Thiagarajan analysis by Gratkowski and Ziolkowski criticises the boundary condition used at the outer radius of the ring conductor and changes it by setting the vector potential to zero at the outer radius of the ring. It is shown that: (i) the boundary condition used by Thiagarajan is an exact analytical result from classical physics, arising from interface field continuity criterion, (ii) setting the vector potential to zero at the outer radius of the ring is not a physically valid boundary condition, and (iii) it changes the boundary value problem entirely with no comparison to the analysis commented upon (which is valid mathematically and physically).

中文翻译：

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对Gratkowski和Ziolkowski的“关于具有矩形横截面的环形导体内瞬态，扩散场的解析解（IET SMT 2008 Vol。2 No. 5）的评论”的回应

讨论了具有矩形横截面的环形导体内部瞬态，扩散场的解析解。V. Thiagarajan的论文中提供了一些细节，并进行了其他说明。Gratkowski和Ziolkowski关于Thiagarajan分析的评论文章批评了在环形导体外半径处使用的边界条件，并通过将矢量电势在环形外半径处设置为零来改变边界条件。结果表明：（i）Thiagarajan使用的边界条件是经典物理学的精确分析结果，是由界面场连续性准则引起的；（ii）将矢量电势在环的外半径处设置为零在物理上不是有效边界条件