b'\n_START_ARTICLE_\nBio-Savaro d\xc4\x97snis\n_START_PARAGRAPH_\nBio-Savaro d\xc4\x97snis \xe2\x80\x93 vienas svarbiausi\xc5\xb3 elektromagnetizmo d\xc4\x97sni\xc5\xb3, naudojamas bet kokios formos laidininko kuriamo magnetinio lauko indukcijai apskai\xc4\x8diuoti:_NEWLINE_\\mbox{d}\\vec{B}=\\frac{\\mu_0I\\left(\\mbox{d}\\vec{l}\\times\\vec{r}\\right)}{4\\pi{r^3}}\n_START_SECTION_\nBio-Savaro d\xc4\x97snio taikymas\n_START_PARAGRAPH_\nDa\xc5\xbeniausiai reikia rasti indukcijos modul\xc4\xaf_NEWLINE_\\mbox{d}{B}=\\frac{\\mu_0I\\sin{\\alpha}\\mbox{d}l}{4\\pi{r^2}}\n_START_SECTION_\nTiesaus plono laidininko magnetin\xc4\x97 indukcija\n_START_PARAGRAPH_\nPagal pateikt\xc4\x85 br\xc4\x97\xc5\xbein\xc4\xaf galima u\xc5\xbera\xc5\xa1yti:_NEWLINE_\\begin{align}_NEWLINE_l&=R\\operatorname{ctg{\\alpha}}\\\\_NEWLINE_\\mbox{d}l&=-\\frac{R\\mbox{d}\\alpha}{\\sin^2{\\alpha}}\\\\_NEWLINE_r&=\\frac{R}{\\sin{\\alpha}}\\\\\\end{align}_NEWLINE_Integruojama nuo \\alpha_1\\; iki \\alpha_2\\;. Kadangi laidininkas be galo ilgas, tai \\alpha_1\\to0, o \\alpha_2\\to\\pi; gaunama, kad_NEWLINE_B=\\left|-\\frac{\\mu_0I}{4\\pi{R}}\\int_0^{\\pi}\\sin{\\alpha}\\mbox{d}\\alpha\\right|=\\frac{\\mu_0I}{2\\pi{R}}\n_START_SECTION_\nPlono \xc5\xbeiedo (apvijos) magnetin\xc4\x97 indukcija\n_START_PARAGRAPH_\nPagal pateikt\xc4\x85 br\xc4\x97\xc5\xbein\xc4\xaf galima u\xc5\xbera\xc5\xa1yti:_NEWLINE_\\begin{align}_NEWLINE_r&=\\sqrt{h^2+R^2}\\\\_NEWLINE_\\sin{\\alpha}&=\\frac{R}{\\sqrt{h^2+R^2}}\\\\_NEWLINE_\\end{align}_NEWLINE_Suintegravus gaunama, kad_NEWLINE_\\begin{align}_NEWLINE_B&=\\left|\\frac{\\mu_0IR}{4\\pi}\\cdot2\\int_0^{\\pi{R}}\\frac{\\mbox{d}l}{\\left(h^2+R^2\\right)^{3/2}}\\right|=\\frac{\\mu_0IR^2}{2\\left({h^2+R^2}\\right)^{3/2}}=\\\\_NEWLINE_&=\\frac{\\mu_0I\\sin^3{\\alpha}}{2R}\\end{align}_NEWLINE_Pastaba: kadangi apeinant vis\xc4\x85 plon\xc4\x85 ilgio l=2\\pi{R}\\; \xc5\xbeied\xc4\x85 atstumas r\\; nekinta, tai integravimas yra tik formalumas, nes pakanka gaut\xc4\x85j\xc4\x85 Bio-Savaro d\xc4\x97snio i\xc5\xa1rai\xc5\xa1k\xc4\x85 padauginti i\xc5\xa1 2\\pi{R}\\;.\n_START_SECTION_\nSolenoido magnetin\xc4\x97 indukcija\n_START_PARAGRAPH_\nLaikoma, kad solenoid\xc4\x85 sudaro apvijos, priglaustos viena prie kitos, bet ne i\xc5\xa1tisinis spirale susuktas laidas. Pa\xc5\xbeym\xc4\x97ta \\angle{NCA}=\\alpha, \\angle{DCA}=\\alpha_1, \\angle{BCA}=\\alpha_2._NEWLINE_Viena apvija kuria indukcij\xc4\x85_NEWLINE_\\mbox{d}B_0=\\frac{\\mu_0I\\sin^3{\\alpha}}{2R}_NEWLINE_l\\; ilgio fragmento dalis \\mbox{d}h\\; ta\xc5\xa1ke C kuria indukcij\xc4\x85. Ji priklauso nuo toje dalyje esan\xc4\x8di\xc5\xb3 apvij\xc5\xb3 skai\xc4\x8diaus_NEWLINE_\\mbox{d}N=\\frac{N}{l}\\cdot\\mbox{d}h_NEWLINE_Tod\xc4\x97l dalis \\mbox{d}h\\; kuria indukcij\xc4\x85_NEWLINE_\\mbox{d}B=\\frac{\\mu_0IN\\sin^3{\\alpha}}{2lR}\\mbox{d}h_NEWLINE_Pagal pateikt\xc4\x85 br\xc4\x97\xc5\xbein\xc4\xaf galima u\xc5\xbera\xc5\xa1yti:_NEWLINE_\\begin{align}_NEWLINE_h&=R\\operatorname{ctg{\\alpha}}\\\\_NEWLINE_\\mbox{d}h&=-\\frac{R\\mbox{d}\\alpha}{\\sin^2{\\alpha}}\\end{align}_NEWLINE_Integruojama nuo \\alpha_1\\; iki \\alpha_2\\;. Kadangi solenoidas be galo ilgas, tai \\alpha_1\\to0, o \\alpha_2\\to\\pi; gaunama, kad_NEWLINE_B=\\left|-\\frac{\\mu_0IN}{2l}\\int_0^{\\pi}\\sin{\\alpha}\\mbox{d}\\alpha\\right|=\\frac{\\mu_0IN}{l}=\\mu_0In_NEWLINE__NEWLINE_kur n\\; \xe2\x80\x93 solenoido apvij\xc5\xb3 skai\xc4\x8dius ilgio vienete_NEWLINE_Pastaba: \xc5\xa1ioje formul\xc4\x97je n\xc4\x97ra dyd\xc5\xbeio h\\;, o tai rei\xc5\xa1kia, kad ilgos rit\xc4\x97s dalyse, esan\xc4\x8diose toli nuo jos gal\xc5\xb3, magnetin\xc4\x97 indukcija nekinta einant tiese CA. Sud\xc4\x97tingesni skai\xc4\x8diavimai rodo, kad indukcija tose dalyse nekinta ir einant skersai rit\xc4\x97s. Vadinasi, \xc5\xa1iose dalyse sukuriamas vienalytis magnetinis laukas._NEWLINE__NEWLINE_\xc5\xa0ias formules taip pat galima gauti ir naudojantis Ampero d\xc4\x97sniu, kuris taip pat naudojamas bet kokios formos laidininko kuriamo magnetinio lauko indukcijai nustatyti.'