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-178 SPHERICAL HARMONICS. [146.
N'ụzọ dị otú a, anyị nwere ike nyochaa Y i n'ime akụkụ ya conjugate harmonics site na ọnụ ọgụgụ nwere njedebe nke ụkpụrụ achọpụtara na isi ihe ahọpụtara na okirikiri.
Ngwa nke Spherical Harmonic Analysis na Mkpebi nke nkesa ọkụ eletrik na gburugburu na ihe fọrọ nke nta ka ọ bụrụ Spherical Ndị na-eduzi n'okpuru Action nke ndị agha eletrik na-apụ apụ ama ama.
146.] Anyị ga-eche na akụkụ ọ bụla nke electrified usoro nke na-eme ihe na-eduzi dị n'ebe dị anya site na etiti nke onye nduzi karịa akụkụ dị anya nke onye nduzi n'onwe ya, ma ọ bụ, ma ọ bụrụ na onye nduzi bụ okirikiri, karịa radius nke gburugburu.
Mgbe ahụ ike nke usoro mpụga, na isi n'ime nke a anya, nwere ike gbasaa n'usoro nke harmonics siri ike nke dị mma ogo y = A ^ + ^ r YI + & c + j . j. ^ (70)
Enwere ike n'ihi onye na-eduzi ya na isi ya nwere ike ịbụ gbasaa na usoro nke harmonics siri ike nke otu ụdị, ma nke ogo na-adịghị mma
(71)
N'elu nke onye na-eduzi ihe nwere ike na-adịgide adịgide na nhata, sị, ka C. Ka anyị buru ụzọ chee na onye nduzi okirikiri na nke radius a. Mgbe ahụ na-etinye r = a, anyị nwere U+ ~ F = C, ma ọ bụ, equating ọnụọgụgụ nke ogo dị iche iche,
3 Q = a (C-AJ,
JB 1 =-a^A 19 (72)
_#. =- + ! ^.
Ngụkọta ụgwọ ọkụ eletrik na onye nduzi bụ BQ.
Enwere ike ịchọta njupụta elu-njupụta n'ebe ọ bụla nke gburugburu site na nha anya
dV du
4 770- = -- -y-
Dr Dr
i Y i. (73)
Nkesa ọkụ eletrik na ihe na-eduzi ihe fọrọ nke nta ka ọ bụrụ Spherical. Ka nha nha nke elu nke onye nduzi ahụ dị
r = a (l+JF), (74)
