Toroidal Metamaterials by Arash Ahmadivand & Burak Gerislioglu & Zeinab Ramezani

Author:Arash Ahmadivand & Burak Gerislioglu & Zeinab Ramezani
Language: eng
Format: epub
ISBN: 9783030582883
Publisher: Springer International Publishing

(4.149)

(4.150)

which obey the following:

(4.151)

and relations:

(4.152)

Considering (4.149) and (4.150) at the order of O(1/r2) (where ):

(4.153)

(4.154)

(4.155)

(4.156)

Therefore, from (2.​88), (2.​89), and (4.156), the leading contributions to and on the order of O(1/r2) can be found as:

(4.157)

and

(4.158)

The descriptions of and to the order of O(1/r2) in terms of time derivatives of radii (i.e., double-superscript quantities) can be obtained through the use of (4.109)–(4.111) and considering the even and odd contributions to the sum over l. Hence:

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