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I'm having a hard time following one part of Bethe "Theory of diffraction by small holes" paper, which can be found here: https://web.stanford.edu/class/ee349/Handouts/Bethe_PR1944.pdf

At the end of page 167 he uses the fact that an uniformly polarized ellipsoid creates a constant field inside, which is the desired solution for the boundary conditions in the apperture.

He then says that the surface density of dipoles is proportional to "the ordinate", which is then said to be proportional to $\mu=(a^2-r'^2)^{1/2}$. Why is that?

Finally, he states that the surface charge density is proportional to $H_0· \nabla \mu$; again, why?

Thanks in advance.

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  • $\begingroup$ It is in Stratton chapter 3 sections 25,26,27 but if you want to understand in more detail how to excite waveguides through holes then Collin chapter 7.3 in Field Theory of Guided Waves is more modern and systematic, but is less physically intuitive. $\endgroup$
    – hyportnex
    Commented Jun 17 at 10:16
  • $\begingroup$ You are right, I just saw those sections in Stratton after the post. I have edited. Thanks $\endgroup$
    – Fernando
    Commented Jun 17 at 10:57
  • $\begingroup$ Nobody able to answer this question? $\endgroup$
    – Fernando
    Commented Oct 31 at 23:45

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