Analytically Regularized Evaluation of the Coupling of Planar Concentric Conducting Rings

Round 1

Reviewer 1 Report

The paper is written and organized well. The paper may be accepted for publication.  The only comment is that the error showcased in results, how comparable it is with other exiting methods e.g., analytical or power series.

Author Response

I would like to thank the reviewer for the gratifying comment. 

To the best of author's knowledge, there is not analytical solution to be compared with the proposed method.

As regard to the power series, there are two possibilities: using a power series "as is", would lead to a much worse convergence of the error, in particular with reference to the azimuthal component. This is due to the fact that a power series converges very slowly to a diverging function, exhibiting the well known Gibbs phenomenon.

A better option would be using a power series divided by the weighting function p(r). As a matter of fact, in this case the convergnece would be the same as that of the proposed method. On the other hand the transform of the expansion functions would not be analytical, which is a very important feature of the proposed method.

Reviewer 2 Report

The author presented the analysis of infinitesimally thin coupled perfectly conducting rings. Overall, it's a good analytical paper, however the reviewer have the following comments:

1. The English style and grammar needs to be improved of this paper. The English language should be checked thoroughly.

2. The authors mentioned geometry 1, 2, 3, and 4 in Fig. 4, however, the reviewer did not find any references of those geometries.

2. Please, put figures 5, 6, 7, 8, and 9 before the references and explain those in more details and intuitively for the peers.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf