{"id":66954,"date":"2023-02-28T06:17:28","date_gmt":"2023-02-28T05:17:28","guid":{"rendered":"https:\/\/botland.com.pl\/blog\/regula-prawej-dloni-poznaj-jej-zasade\/"},"modified":"2023-08-02T13:21:52","modified_gmt":"2023-08-02T11:21:52","slug":"pravidlo-prave-ruky-poznejte-jeho-princip","status":"publish","type":"post","link":"https:\/\/botland.cz\/blog\/pravidlo-prave-ruky-poznejte-jeho-princip\/","title":{"rendered":"Pravidlo prav\u00e9 ruky – poznejte jeho princip"},"content":{"rendered":"\u010cas \u010dten\u00ed:<\/span> 5<\/span> min.<\/span><\/span>\t\t
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N\u011bkte\u0159\u00ed \u010dten\u00e1\u0159i se s t\u00edmto pojmem ji\u017e jist\u011b setkali, ale najdou se i tac\u00ed, kte\u0159\u00ed se s n\u00edm teprve setkaj\u00ed. Nau\u010dte se tedy teoretick\u00e1 i praktick\u00e1 tajemstv\u00ed pravidla prav\u00e9 ruky!<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Pravidlo prav\u00e9 ruky v praxi<\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Tento \u010dl\u00e1nek p\u0159edstavuje pravidlo prav\u00e9 ruky, jeho fyzik\u00e1ln\u00ed interpretaci a matematick\u00fd popis. Je tak\u00e9 nast\u00edn\u011bno praktick\u00e9 pou\u017eit\u00ed pravidla prav\u00e9 ruky v klasick\u00e9 elektrodynamice.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Pravidlo prav\u00e9 ruky ve fyzice<\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Pravidlo prav\u00e9 ruky je jedno z mnemotechnick\u00fdch pravidel b\u011b\u017en\u011b pou\u017e\u00edvan\u00fdch ve fyzice, pomoc\u00ed kter\u00e9ho lze identifikovat sm\u011bry sil v trojrozm\u011brn\u00e9m prostoru. Pravidlo prav\u00e9 ruky vyvinul v 19. stolet\u00ed John Ambrose Fleming, anglick\u00fd fyzik specializuj\u00edc\u00ed se na elektrotechniku a radiotechniku, kter\u00fd je zn\u00e1m\u00fd tak\u00e9 d\u00edky v\u00fdvoji prvn\u00ed elektronky, vakuov\u00e9 diody. Pomoc\u00ed tohoto pravidla je mo\u017en\u00e9 ur\u010dit sm\u011br jednoho ze t\u0159\u00ed hledan\u00fdch parametr\u016f na z\u00e1klad\u011b znalosti dal\u0161\u00edch dvou, co\u017e lze aplikovat na magnetick\u00e9 pole, elektrodynamickou s\u00edlu a proud. Existuje n\u011bkolik variant pravidla prav\u00e9 ruky, kter\u00e9 si v tomto \u010dl\u00e1nku vysv\u011btl\u00edme.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Pravidlo prav\u00e9 ruky. Zdroj: wikipedia.org<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Pravidlo prav\u00e9 ruky pro indukovanou elektromotorickou s\u00edlu<\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Jedn\u00edm z probl\u00e9m\u016f ve fyzice, na kter\u00fd lze aplikovat pravidlo prav\u00e9 ruky, je indukce elektromotorick\u00e9 s\u00edly (nap\u011bt\u00ed zdroje) v magnetick\u00e9m poli. Tento jev se naz\u00fdv\u00e1 elektromagnetick\u00e1 indukce a je pops\u00e1n z\u00e1konem elektromagnetick\u00e9 indukce, kter\u00fd experiment\u00e1ln\u011b vyvinul Michael Faraday v roce 1831. Podle Faradayova z\u00e1kona um\u00edst\u00edme-li vodi\u010d (nap\u0159. m\u011bd\u011bn\u00fd dr\u00e1t) do magnetick\u00e9ho pole a pohybujeme-li j\u00edm v tomto poli, iniciujeme v n\u011bm tok elektrick\u00e9ho proudu. Ve Faradayov\u011b z\u00e1kon\u011b, kter\u00fdm lze popsat elektromotorickou s\u00edlu indukovanou v c\u00edvce, existuje souvislost mezi pravidlem prav\u00e9 ruky, kter\u00e9 je vyj\u00e1d\u0159eno vztahem:<\/p>\n

(1.1) kde:<\/span>
e(t) – elektromotorick\u00e1 s\u00edla indukce [V] = [J\/C];
N – po\u010det z\u00e1vit\u016f tvo\u0159\u00edc\u00edch c\u00edvku;
– tok magnetick\u00e9ho pole [Wb] = [T*m2<\/span>];
t – \u010das [s].<\/p>\n

V trojrozm\u011brn\u00e9m sou\u0159adn\u00e9m syst\u00e9mu jsou jednotliv\u00e9 osy, kter\u00e9 jej tvo\u0159\u00ed, tj. X, Y a Z jsou na sebe kolm\u00e9, tak\u017ee takov\u00fd sou\u0159adnicov\u00fd syst\u00e9m lze zazimovat pravou rukou tak, \u017ee palec, prvn\u00ed prst a druh\u00fd prst srovn\u00e1me. Nejprve narovn\u00e1me prav\u00fd palec. Pot\u00e9 narovnejte prvn\u00ed a druh\u00fd prst tak, aby sm\u011b\u0159ovaly stejn\u00fdm sm\u011brem rovnob\u011b\u017en\u011b a spolu s narovnan\u00fdm palcem tvo\u0159ily prav\u00fd \u00fahel. Nyn\u00ed druh\u00fd prst p\u0159elo\u017e\u00edme sm\u011brem dovnit\u0159 ruky tak, aby s prvn\u00edm prstem a palcem sv\u00edral prav\u00fd \u00fahel. Ka\u017ed\u00fd prst pak bude ukazovat ve sm\u011brech os, kter\u00e9 tvo\u0159\u00ed trojrozm\u011brn\u00fd sou\u0159adn\u00fd syst\u00e9m.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Pravidlo prav\u00e9 ruky a Lorentzova s\u00edla<\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Nabit\u00e1 \u010d\u00e1stice obsahuje elektrick\u00fd n\u00e1boj. Pokud se nabit\u00e1 stacion\u00e1rn\u00ed \u010d\u00e1stice nach\u00e1z\u00ed v magnetick\u00e9m poli a pohybuje se rovnob\u011b\u017en\u011b s jeho \u010darami, pak s n\u00ed magnetick\u00e9 pole neinteraguje. Naproti tomu kdy\u017e \u010d\u00e1stice zm\u011bn\u00ed sm\u011br sv\u00e9ho pohybu a vytvo\u0159\u00ed nenulov\u00fd \u00fahel mezi vektorem sv\u00e9 rychlosti a vektorem indukce magnetick\u00e9ho pole, p\u016fsob\u00ed na ni s\u00edla magnetick\u00e9ho pole. Takov\u00fd jev se naz\u00fdv\u00e1 Lorentzova s\u00edla interakce. Lorentzovu s\u00edlu vypo\u010d\u00edt\u00e1me z rovnice (2.1):<\/p>\n

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(2.1) kde:<\/span>
– Lorentzova s\u00edla [N]
– elektrick\u00fd n\u00e1boj [C]
– rychlost nabit\u00fdch \u010d\u00e1stic [m\/s]
– indukce magnetick\u00e9ho pole [T]
– \u00fahel mezi vektorem rychlosti nabit\u00fdch \u010d\u00e1stic a vektorem indukce magnetick\u00e9ho pole [\u00b0].<\/p>\n

Z matematick\u00e9ho popisu Lorentzovy s\u00edly vypl\u00fdv\u00e1, \u017ee nabit\u00e1 \u010d\u00e1stice pohybuj\u00edc\u00ed se rovnob\u011b\u017en\u011b nebo protib\u011b\u017en\u011b se silami magnetick\u00e9ho pole nebude Lorentzovou silou ovlivn\u011bna (nulov\u00fd \u00fahel mezi vektory rychlosti \u010d\u00e1stice a indukce magnetick\u00e9ho pole), a to ani v p\u0159\u00edpad\u011b, \u017ee magnetick\u00e9 pole je velmi siln\u00e9. Pravidlo prav\u00e9 ruky tak\u00e9 pom\u00e1h\u00e1 ilustrovat Lorentzovu s\u00edlu. Pro ur\u010den\u00ed sm\u011bru magnetick\u00e9ho pole na kladn\u011b nabitou \u010d\u00e1stici p\u0159edpokl\u00e1dejme, \u017ee palec bude ukazovat ve sm\u011bru vektoru rychlosti \u010d\u00e1stice, prvn\u00ed prst bude ukazovat ve sm\u011bru indukce magnetick\u00e9ho pole a druh\u00fd prst bude ukazovat ve sm\u011bru v\u00fdsledn\u00e9 Lorentzovy s\u00edly. Na z\u00e1porn\u011b nabit\u00e9 \u010d\u00e1stice p\u016fsob\u00ed Lorentzova s\u00edla opa\u010dn\u00fdm sm\u011brem ne\u017e na kladn\u011b nabit\u00e9 \u010d\u00e1stice.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Magnetick\u00e1 s\u00edla vyvolan\u00e1 pr\u016ftokem elektrick\u00e9ho proudu v p\u0159\u00edmo\u010dar\u00e9m vodi\u010di<\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Elektrick\u00fd proud lze nejjednodu\u0161eji definovat jako uspo\u0159\u00e1dan\u00fd pohyb nosi\u010d\u016f elektrick\u00e9ho n\u00e1boje. Kdy\u017e vodi\u010dem prot\u00e9k\u00e1 elektrick\u00fd proud, vytv\u00e1\u0159\u00ed se kolem n\u011bj magnetick\u00e9 pole, kter\u00e9 na n\u011bj p\u016fsob\u00ed. I zde m\u016f\u017eeme pou\u017e\u00edt pravidlo prav\u00e9 ruky, ale jin\u00fdm, mo\u017en\u00e1 je\u0161t\u011b jednodu\u0161\u0161\u00edm zp\u016fsobem. Ruka by m\u011bla b\u00fdt polo\u017eena tak, aby prsty 1, 2, 3 a 4 byly sto\u010deny do dlan\u011b a palec byl rovn\u00fd. P\u0159i obj\u00edm\u00e1n\u00ed vodi\u010de, kter\u00fdm prot\u00e9k\u00e1 proud, bude palec ukazovat ve sm\u011bru prot\u00e9kaj\u00edc\u00edho proudu a ostatn\u00ed prsty budou ukazovat ve sm\u011bru magnetick\u00fdch silo\u010dar indukovan\u00fdch kolem tohoto vodi\u010de. Takov\u00fd jev lze popsat vztahem:<\/p>\n


(3.1) kde:
FB<\/span> – intenzita magnetick\u00e9ho pole kolem vodi\u010de, kter\u00fdm prot\u00e9k\u00e1 proud [N];
B – indukce magnetick\u00e9ho pole kolem vodi\u010de, kter\u00fdm prot\u00e9k\u00e1 proud [T];
I – proud tekouc\u00ed ve vodi\u010di [A];
l – d\u00e9lka kabelu [m];
– \u00fahel mezi vektorem indukce magnetick\u00e9ho pole a vektorem d\u00e9lky vodi\u010de vedouc\u00edho proud [\u00b0].<\/p>\n

Pokud budeme tok proudu pova\u017eovat za pohyb kladn\u00fdch nosi\u010d\u016f n\u00e1boje, zjist\u00edme, \u017ee se proud pohybuje sm\u011brem nahoru. Proto\u017ee b\u011b\u017en\u00fd proud se skl\u00e1d\u00e1 z kladn\u00fdch nosi\u010d\u016f n\u00e1boje, lze stejn\u00fd vodi\u010d, kter\u00fdm prot\u00e9k\u00e1 proud, popsat tak\u00e9 jako vodi\u010d, kter\u00fdm prot\u00e9k\u00e1 proud v podob\u011b pohybu z\u00e1porn\u00fdch nosi\u010d\u016f n\u00e1boje sm\u011brem dol\u016f. P\u0159esto\u017ee se tyto proudy pohybuj\u00ed v opa\u010dn\u00fdch sm\u011brech, p\u016fsob\u00ed na vodi\u010d jedin\u00e1 magnetick\u00e1 s\u00edla. S\u00edla tedy p\u016fsob\u00ed stejn\u00fdm sm\u011brem bez ohledu na to, zda uva\u017eujeme tok kladn\u00fdch nebo z\u00e1porn\u00fdch nosi\u010d\u016f n\u00e1boje. Uva\u017eujeme-li tok z\u00e1porn\u00fdch nosi\u010d\u016f n\u00e1boje, pravidlo prav\u00e9 ruky nazna\u010duje sm\u011br s\u00edly doleva; z\u00e1porn\u00e9 znam\u00e9nko v\u0161ak v\u00fdsledek obrac\u00ed a nazna\u010duje, \u017ee sm\u011br magnetick\u00e9 s\u00edly ve skute\u010dnosti vede doprava. Pokud naopak uva\u017eujeme tok n\u00e1boj\u016f ve dvou r\u016fzn\u00fdch vodi\u010d\u00edch, z nich\u017e jeden m\u00e1 kladn\u00e9 n\u00e1boje proud\u00edc\u00ed vzh\u016fru a druh\u00fd z\u00e1porn\u00e9, sm\u011br magnetick\u00fdch sil nebude stejn\u00fd, proto\u017ee uva\u017eujeme dv\u011b r\u016fzn\u00e9 fyzik\u00e1ln\u00ed situace. V prvn\u00edm vodi\u010di proud\u011bn\u00ed kladn\u00fdch n\u00e1boj\u016f sm\u011brem nahoru znamen\u00e1, \u017ee z\u00e1porn\u00e9 n\u00e1boje proud\u00ed dol\u016f. Pravidlo prav\u00e9 ruky n\u00e1m \u0159\u00edk\u00e1, \u017ee magnetick\u00e1 s\u00edla bude sm\u011b\u0159ovat spr\u00e1vn\u00fdm sm\u011brem. Ve druh\u00e9m vodi\u010di proud\u00ed z\u00e1porn\u00e9 n\u00e1boje nahoru, co\u017e znamen\u00e1, \u017ee kladn\u00e9 n\u00e1boje proud\u00ed dol\u016f. Pravidlo prav\u00e9 ruky tedy znamen\u00e1, \u017ee magnetick\u00e1 s\u00edla je sm\u011brov\u00e1na doleva.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Pravidlo prav\u00e9 ruky versus Lenz\u016fv z\u00e1kon<\/h2><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Lenz\u016fv z\u00e1kon se \u010dasto jev\u00ed jako neintuitivn\u00ed, proto\u017ee vy\u017eaduje pochopen\u00ed interakce mezi magnetismem a elektrick\u00fdm polem v r\u016fzn\u00fdch situac\u00edch. Lenz\u016fv z\u00e1kon \u0159\u00edk\u00e1, \u017ee sm\u011br proudu indukovan\u00e9ho v uzav\u0159en\u00e9 vodiv\u00e9 smy\u010dce m\u011bn\u00edc\u00edm se magnetick\u00fdm polem (podle Faradayova induk\u010dn\u00edho z\u00e1kona) je takov\u00fd, \u017ee sekund\u00e1rn\u00ed magnetick\u00e9 pole vytvo\u0159en\u00e9 indukovan\u00fdm proudem je proti p\u016fvodn\u00ed zm\u011bn\u011b magnetick\u00e9ho pole, kter\u00e9 ho vyvolalo. To znamen\u00e1, \u017ee kdy\u017e se zm\u011bn\u00ed tok magnetick\u00e9ho pole kolem vodi\u010de v uzav\u0159en\u00e9 smy\u010dce, indukuje se ve smy\u010dce proud. Indukovan\u00fd proud vytv\u00e1\u0159\u00ed sekund\u00e1rn\u00ed magnetick\u00e9 pole, kter\u00e9 je opa\u010dn\u00e9 ne\u017e prim\u00e1rn\u00ed zm\u011bna toku, je\u017e iniciovala indukovan\u00fd proud. S\u00edla magnetick\u00e9ho pole proch\u00e1zej\u00edc\u00edho c\u00edvkou dr\u00e1tu ur\u010duje magnetick\u00fd tok. Tok magnetick\u00e9ho pole z\u00e1vis\u00ed \u00fam\u011brn\u011b na indukci magnetick\u00e9ho pole, plo\u0161e ohrani\u010den\u00e9 vodi\u010dem a relativn\u00ed orientaci magnetick\u00e9ho pole a c\u00edvky podle vztahu (4.1):<\/p>\n


(4.1) kde:
= tok magnetick\u00e9ho pole [Wb] = [T*m2<\/span>].
B – indukce magnetick\u00e9ho pole [T].
S = plocha smy\u010dky ohrani\u010den\u00e1 dr\u00e1tem[m2<\/span>].
– \u00fahel mezi vektorem indukce magnetick\u00e9ho pole a vektorem povrchu smy\u010dky ohrani\u010den\u00e9 vodi\u010dem [\u00b0].<\/p>\n

Abychom pochopili, jak Lenz\u016fv z\u00e1kon ovlivn\u00ed chov\u00e1n\u00ed takov\u00e9ho syst\u00e9mu, mus\u00edme nejprve ur\u010dit, zda po\u010d\u00e1te\u010dn\u00ed magnetick\u00e9 pole roste nebo kles\u00e1. Jak se severn\u00ed magnetick\u00fd p\u00f3l p\u0159ibli\u017euje ke smy\u010dce, doch\u00e1z\u00ed ke zv\u00fd\u0161en\u00ed intenzity magnetick\u00e9ho pole. S rostouc\u00edm magnetick\u00fdm polem se indukovan\u00fd proud a v\u00fdsledn\u00e9 indukovan\u00e9 magnetick\u00e9 pole stav\u00ed proti p\u016fvodn\u00edmu magnetick\u00e9mu poli a zmen\u0161uje ho. To znamen\u00e1, \u017ee prim\u00e1rn\u00ed a sekund\u00e1rn\u00ed magnetick\u00e9 pole budou p\u016fsobit v opa\u010dn\u00fdch sm\u011brech. Kdy\u017e se st\u00e1vaj\u00edc\u00ed magnetick\u00e9 pole zmen\u0161uje, indukovan\u00fd proud a v\u00fdsledn\u00e9 indukovan\u00e9 magnetick\u00e9 pole p\u016fsob\u00ed proti p\u016fvodn\u00edmu, zmen\u0161uj\u00edc\u00edmu se magnetick\u00e9mu poli a zesiluje ho. Indukovan\u00e9 magnetick\u00e9 pole m\u00e1 tedy stejn\u00fd sm\u011br jako p\u016fvodn\u00ed magnetick\u00e9 pole. Abychom mohli pou\u017e\u00edt pravidlo prav\u00e9 ruky pro Lenz\u016fv z\u00e1kon, mus\u00edme ur\u010dit, zda magnetick\u00e9 pole proch\u00e1zej\u00edc\u00ed smy\u010dkou s proudem roste nebo kles\u00e1. Magnety vytv\u00e1\u0159ej\u00ed magnetick\u00e9 silo\u010d\u00e1ry, kter\u00e9 se t\u00e1hnou od severn\u00edho magnetick\u00e9ho p\u00f3lu sm\u011brem k ji\u017en\u00edmu magnetick\u00e9mu p\u00f3lu – magnetick\u00e9 silo\u010d\u00e1ry jsou uzav\u0159en\u00e9. Pokud se magnetick\u00e9 pole zv\u011bt\u0161\u00ed, sm\u011br vektoru indukovan\u00e9ho magnetick\u00e9ho pole bude opa\u010dn\u00fd. Pokud magnetick\u00e9 pole ve smy\u010dce kles\u00e1, vektor indukovan\u00e9ho magnetick\u00e9ho pole se objev\u00ed ve stejn\u00e9m sm\u011bru, aby nahradil pokles p\u016fvodn\u00edho magnetick\u00e9ho pole. Kdy\u017e um\u00edst\u00edte palec ve sm\u011bru indukovan\u00e9ho magnetick\u00e9ho pole a ostatn\u00ed prsty sto\u010d\u00edte do dlan\u011b, uk\u00e1\u017ee se sm\u011br indukovan\u00e9ho proudu.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

N\u011bkte\u0159\u00ed \u010dten\u00e1\u0159i se s t\u00edmto pojmem ji\u017e jist\u011b setkali, ale najdou se i tac\u00ed, kte\u0159\u00ed se s n\u00edm teprve setkaj\u00ed. Nau\u010dte se tedy teoretick\u00e1 i praktick\u00e1 tajemstv\u00ed pravidla prav\u00e9 ruky! Pravidlo prav\u00e9 ruky v praxi Tento \u010dl\u00e1nek p\u0159edstavuje pravidlo prav\u00e9 ruky, jeho fyzik\u00e1ln\u00ed interpretaci a matematick\u00fd popis. Je tak\u00e9 nast\u00edn\u011bno praktick\u00e9 pou\u017eit\u00ed pravidla prav\u00e9 ruky […]<\/p>\n","protected":false},"author":22,"featured_media":63423,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[548,549],"tags":[],"class_list":["post-66954","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-elektronika-cs","category-kompendium-cs"],"acf":[],"yoast_head":"\nPravidlo prav\u00e9 ruky - poznejte jeho princip - Botland<\/title>\n<meta name=\"description\" content=\"Pravidlo prav\u00e9 ruky je jedn\u00edm ze z\u00e1kladn\u00edch princip\u016f popisuj\u00edc\u00edch teoretick\u00e9 i praktick\u00e9 mechanismy p\u016fsoben\u00ed v klasick\u00e9 elektrodynamice.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/botland.cz\/blog\/pravidlo-prave-ruky-poznejte-jeho-princip\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pravidlo prav\u00e9 ruky - 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