Abstract
In Sect. 4.2 an expression (4.12) was derived for the resonant frequency shift in a waveguide, when a small metal sphere of radius r was placed onto the lower conducting surface of a waveguide with electric field E 0. In deriving that expression the induced electric dipole moment was assumed to be given by
The fact that the conducting sphere is in contact with the lower conducting surface makes (B.1) a poor approximation for the induced dipole moment. In this Appendix, the method of images is used to derive a better model for the induced dipole. Using this model, the dipole moment acquires an extra multiplicative factor c 0 = 2ζ(3) ≈ 2.404, so that using the induced dipole given by p = coE 0 r 3, a more accurate expression for the cavity frequency shift measurements is given by the relation
where we use the notation of Chap, 4, in which E is the root-mean-square magnitude of the electric field inside the cavity; ζ(n) is the Riemann Zeta Function of argument n (see Chap. 23 of [132]).
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© 1999 Springer-Verlag Berlin Heidelberg
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(1999). Conducting Sphere on a Grounded Surface. In: Binding and Scattering in Two-Dimensional Systems. Lecture Notes in Physics Monographs, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47937-6_10
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DOI: https://doi.org/10.1007/3-540-47937-6_10
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