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Vlasne sila Lorenca 2 Sila Lorenca v teoriyi vidnosnosti 3 Funkciya Gamiltona 4 Ruh zaryadzhenoyi chastinki v odnoridnih polyah 5 Div takozh 6 PrimitkiVivedennya iz vikoristannyam zakonu Kulona ta specialnoyi teoriyi vidnosnosti RedaguvatiPoperedni peretvorennya Redaguvati Poperedni peretvorennya Peretvorennya Lorenca dlya radius vektora r r G u u r c 2 g u t displaystyle mathbf r mathbf r Gamma mathbf u frac mathbf u cdot mathbf r c 2 gamma mathbf u t nbsp g 1 1 u 2 c 2 displaystyle gamma frac 1 sqrt 1 frac u 2 c 2 nbsp G g 1 u 2 c 2 g 2 1 g displaystyle Gamma frac gamma 1 frac u 2 c 2 frac gamma 2 1 gamma nbsp u displaystyle mathbf u nbsp vidnosna shvidkist mizh dvoma inercialnimi sistemami vidliku Pri t 0 displaystyle t 0 nbsp viraz peretvoryuyetsya u nastupnij r r G u u r c 2 1 displaystyle mathbf r mathbf r Gamma mathbf u frac mathbf u cdot mathbf r c 2 qquad 1 nbsp Yaksho pidnesti livu i pravu chastinu do kvadratu mozhna bude otrimati r 2 r 2 g 2 c 2 u r 2 2 displaystyle mathbf r 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quad 1 frac Gamma u 2 c 2 gamma right frac mathbf r cdot mathbf v gamma left 1 frac mathbf u cdot mathbf v c 2 right frac gamma 2 mathbf r cdot mathbf u left 1 frac mathbf u cdot mathbf v c 2 right gamma left 1 frac mathbf u cdot mathbf v c 2 right frac mathbf r cdot mathbf v gamma left 1 frac mathbf u cdot mathbf v c 2 right gamma mathbf r cdot mathbf u nbsp Viraz dlya peretvorennya 3 vektora sili pri perehodi do novoyi ISV F g 1 v u c 2 F g u F v c 2 G u u F c 2 5 displaystyle frac mathbf F gamma 1 frac mathbf v cdot mathbf u c 2 mathbf F gamma frac mathbf u mathbf F cdot mathbf v c 2 Gamma mathbf u frac mathbf u cdot mathbf F c 2 qquad 5 nbsp Vlasne sila Lorenca Redaguvati Bazovim virazom dlya analizu vzayemodiyi zaryada Q displaystyle Q nbsp iz deyakim probnim zaryadom q displaystyle q nbsp ye zakon Kulona dlya statichnih zaryadiv u vakuumi vidnosno inercialnoyi sistemi vidliku sho perebuvaye u spokoyi mozhna zapisati sho sila yihnoyi vzayemodiyi dorivnyuye F q Q r 3 r displaystyle mathbf F frac qQ mathbf r 3 mathbf r nbsp Dlya togo shob viznachiti yak bude viglyadati cya sila v inercialnij sistemi vidliku sho ruhayetsya mozhna rozglyanuti nastupnij virtualnij eksperiment Nehaj u vakuumi znahodyatsya dva zaryadi skripleni pruzhinkoyu Zaryadi rozglyadayutsya vidnosno inercialnoyi sistemi vidliku u yakij voni perebuvayut u spokoyi protyagom dosit velikogo promizhku chasu Pruzhinka zabezpechuye statichnist zaryadiv a roztyag pruzhinki chiselno harakterizuye silu vzayemodiyi zaryadiv Yaksho pribrati pruzhinku j rozglyanuti deyake male vidhilennya vid statichnogo stanu napriklad odnogo zaryadu to mozhna proanalizuvati chas za yakij drugij zaryad vidchuye zminu stanu pershogo tim samim eksperimentalno viznachivshi shvidkist rozpovsyudzhennya vzayemodiyi mizh zaryadami Prote v ramkah eksperimentu zaryadi skripleni pruzhinkoyu pro shvidkist rozpovsyudzhennya vzayemodiyi nichogo ne mozhna skazati oskilki sistema ye statichnoyu Takim chinom zakon Kulona yakij opisuye 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mathbf r mathbf u cdot mathbf r frac Qq mathbf r 3 left 1 frac mathbf u cdot mathbf v c 2 right left mathbf r frac 1 c 2 mathbf v times mathbf u times mathbf r right Rightarrow mathbf F frac qQ gamma left mathbf r 2 frac gamma 2 c 2 mathbf u cdot mathbf r 2 right frac 3 2 left mathbf r frac 1 c 2 mathbf v times mathbf u times mathbf r right nbsp de dlya r 2 displaystyle mathbf r 2 nbsp vrahovana rivnist 2 displaystyle 2 nbsp Varto zaznachiti sho hoch 3 vektor sili i zminyuyetsya ale 4 vektor zalishayetsya invariantnim Dali yaksho vvesti poznachennya E Q g r r 2 g 2 c 2 u r 2 3 2 B 1 c u E displaystyle mathbf E frac Q gamma mathbf r left mathbf r 2 frac gamma 2 c 2 mathbf u cdot mathbf r 2 right frac 3 2 quad mathbf B frac 1 c mathbf u times mathbf E nbsp de E displaystyle mathbf E nbsp napruzhenist elektrichnogo polya B displaystyle mathbf B nbsp indukciya magnitnogo polya to z 7 displaystyle 7 nbsp mozhna otrimati F q Q g r r 2 g 2 r u 2 c 2 3 2 q c 2 v Q g u r r 2 g 2 r u 2 c 2 3 2 q E q c v B displaystyle mathbf F q frac Q gamma mathbf r r 2 gamma 2 frac mathbf r cdot mathbf u 2 c 2 frac 3 2 frac q c 2 left mathbf v times frac Q gamma mathbf u times mathbf r r 2 gamma 2 frac mathbf r cdot mathbf u 2 c 2 frac 3 2 right q mathbf E frac q c mathbf v times mathbf B nbsp sho i ye virazom dlya sili Lorenca Zvidsi ochevidno sho magnitne pole relyativistskij efekt sho pov yazanij iz zapiznennyam zmishennya elektrichnogo polya cherez kinechnist shvidkosti rozpovsyudzhennya vzayemodiyi pri rusi jogo dzherela zi shvidkistyu u displaystyle mathbf u nbsp abo chisto kinematichno cherez peretvorennya virazu sili vzayemodiyi pri perehodi vid odniyeyi ISV do inshoyi U vipadku koli zaryad sho stvoryuye pole perebuvaye v spokoyi viraz dlya sili Lorenca perehodit u zakon Kulona Sila Lorenca v teoriyi vidnosnosti RedaguvatiV teoriyi vidnosnosti sila Lorenca zapisuyetsya v kovariantnij formi f i q c F i k u k displaystyle f i frac q c F ik u k nbsp de f i displaystyle f i nbsp 4 vektor sili u k displaystyle u k nbsp 4 shvidkist a F i k displaystyle F ik nbsp 4 tenzor elektromagnitnogo polya Funkciya Gamiltona RedaguvatiHocha sila Lorenca ne ye potencialnoyu oskilki vona zalezhit vid shvidkosti chastinki zaryadzhenu chastinku v elektrichnomu ta magnitnomu polyah mozhna opisati funkciyeyu Gamiltona u viglyadi H p q c A 2 2 m q f displaystyle mathcal H frac mathbf p frac q c mathbf A 2 2m q varphi nbsp de A displaystyle mathbf A nbsp vektornij a f displaystyle varphi nbsp elektrichnij potencial a p displaystyle mathbf p nbsp impuls chastinki Ruh zaryadzhenoyi chastinki v odnoridnih polyah RedaguvatiV odnoridnomu magnitnomu poli zaryadzhena chastinka ruhayetsya po gvintovij liniyi yaku v fizici desho nestrogo chasto nazivayut spirallyu Radius gvintovoyi liniyi ciklotronnij radius viznachayetsya perpendikulyarnoyu do polya skladovoyu pochatkovoyi shvidkosti chastinki Krok gvintovoyi liniyi paralelnoyu do polya skladovoyu pochatkovoyi shvidkosti chastinki Gvintova liniya zakruchena za chi proti godinnikovoyi strilki v zalezhnosti vid znaku zaryadu chastinki Div takozh RedaguvatiPeretvorennya Lorenca Peretvorennya Lorenca dlya poliv Vimiryuvannya shvidkosti siloyu LorencaPrimitki Redaguvati Formuli na cij storinci zapisani v sistemi SGS SGSG Dlya peretvorennya v Mizhnarodnu sistemu velichin ISQ divis Pravila perevodu formul iz sistemi SGS v sistemu ISQ Cya stattya ne mistit posilan na dzherela Vi mozhete dopomogti polipshiti cyu stattyu dodavshi posilannya na nadijni avtoritetni dzherela Material bez dzherel mozhe buti piddano sumnivu ta vilucheno listopad 2011 Otrimano z https uk wikipedia org w index php title Sila Lorenca amp oldid 38993605
