{"id":4799,"date":"2024-11-19T15:19:52","date_gmt":"2024-11-19T14:19:52","guid":{"rendered":"https:\/\/www.zsvltava.cz\/fyzika\/?p=4799"},"modified":"2025-04-09T11:35:23","modified_gmt":"2025-04-09T09:35:23","slug":"matematika-elektromagneticke-indukce","status":"publish","type":"post","link":"https:\/\/www.zsvltava.cz\/fyzika\/?p=4799","title":{"rendered":"Matematika elektromagnetick\u00e9 indukce"},"content":{"rendered":"

Matematick\u00e1 interpretace elektromagnetick\u00e9 indukce vych\u00e1z\u00ed z Faradayova z\u00e1kona (indukovan\u00e9 nap\u011bt\u00ed je \u00fam\u011brn\u00e9 zm\u011bn\u011b magnetick\u00e9ho toku), Lenzova pravidla (sm\u011br indukovan\u00e9ho nap\u011bt\u00ed je proti zm\u011bn\u011b magnetick\u00e9ho toku) a dal\u0161\u00edch vztah\u016f t\u00fdkaj\u00edc\u00edch se pohybu vodi\u010de v magnetick\u00e9m poli, induk\u010dnosti c\u00edvky nebo zm\u011bn proudu v obvodu.<\/strong> <\/p>\n

Elektromagnetick\u00e1 indukce<\/a> je z\u00e1kladem mnoha technologi\u00ed, v\u010detn\u011b gener\u00e1tor\u016f, transform\u00e1tor\u016f, motor\u016f a induk\u010dn\u00edch va\u0159i\u010d\u016f.<\/p>\n

Symbyol Ε p\u0159edstavuje elektromotorick\u00e9 nap\u011bt\u00ed vznik\u00e1 v obvodu vlivem zm\u011bny magnetick\u00e9ho toku podle Faradayova z\u00e1kona elektromagnetick\u00e9 indukce. <\/p>\n

Elektromotorick\u00e9 nap\u011bt\u00ed (EMN) je elektrick\u00e9 nap\u011bt\u00ed generovan\u00e9 zdrojem, jako je baterie nebo gener\u00e1tor, kter\u00e9 poh\u00e1n\u00ed elektrick\u00fd proud v obvodu.<\/em><\/p>\n

1. Faraday\u016fv z\u00e1kon indukce<\/strong><\/p>\n

Faraday\u016fv z\u00e1kon je z\u00e1kladn\u00edm principem elektromagnetick\u00e9 indukce. Tento z\u00e1kon \u0159\u00edk\u00e1, \u017ee indukovan\u00e9 nap\u011bt\u00ed v uzav\u0159en\u00e9m obvodu je \u00fam\u011brn\u00e9 rychl\u00e9 zm\u011bn\u011b magnetick\u00e9ho toku, kter\u00fd proch\u00e1z\u00ed t\u00edmto obvodem.<\/p>\n

  <\/span>   <\/span>\"\[<\/p>\n

2. Magnetick\u00fd tok<\/strong><\/p>\n

Magnetick\u00fd tok je definov\u00e1n jako sou\u010din magnetick\u00e9 indukce B a velikosti plochy \ud835\udc34, kterou toto pole proch\u00e1z\u00ed, a kosinu \u00fahlu mezi sm\u011brem magnetick\u00e9ho pole a norm\u00e1lou k t\u00e9to plo\u0161e.<\/p>\n

  <\/span>   <\/span>\"\[<\/p>\n

3. Lenzovo pravidlo<\/strong><\/p>\n

Lenzovo pravidlo \u0159\u00edk\u00e1, \u017ee sm\u011br indukovan\u00e9ho proudu v obvodu je takov\u00fd, \u017ee jeho magnetick\u00e9 pole p\u016fsob\u00ed proti zm\u011bn\u011b p\u016fvodn\u00edho magnetick\u00e9ho pole. Tedy pokud magnetick\u00fd tok v obvodu roste, indukovan\u00fd proud vytvo\u0159\u00ed magnetick\u00e9 pole, kter\u00e9 tento r\u016fst \u201ebrzd\u00ed\u201c, a pokud magnetick\u00fd tok kles\u00e1, indukovan\u00fd proud ho \u201epodporuje\u201c. Toto pravidlo je vyj\u00e1d\u0159eno z\u00e1porn\u00fdm znam\u00e9nkem v Faradayov\u011b z\u00e1kon\u011b.<\/p>\n

  <\/span>   <\/span>\"\[<\/p>\n

4. Indukovan\u00e9 nap\u011bt\u00ed v pohybuj\u00edc\u00edm se vodi\u010di<\/strong><\/p>\n

Pokud vodi\u010d pohybujeme v magnetick\u00e9m poli, doch\u00e1z\u00ed k indukci nap\u011bt\u00ed v d\u016fsledku pohybu vodi\u010de v magnetick\u00e9m poli.<\/p>\n

  <\/span>   <\/span>\"\[<\/p>\n

5. Indukce v c\u00edvce<\/strong><\/p>\n

Pokud je obvod tvo\u0159en c\u00edvkou, indukovan\u00e9 nap\u011bt\u00ed je zp\u016fsobeno zm\u011bnami v proudu, kter\u00fd proch\u00e1z\u00ed c\u00edvkou. Tento jev je zn\u00e1m\u00fd jako self-indukce. Indukovan\u00e9 nap\u011bt\u00ed v c\u00edvce je p\u0159\u00edmo \u00fam\u011brn\u00e9 zm\u011bn\u011b proudu v \u010dase a induk\u010dnosti c\u00edvky. Induk\u010dnost L z\u00e1vis\u00ed na geometrii c\u00edvky (po\u010det z\u00e1vit\u016f, plocha pr\u016f\u0159ezu a d\u00e9lka c\u00edvky) a na materi\u00e1lu, kter\u00fdm je j\u00e1dro c\u00edvky (nap\u0159. feromagnetick\u00fd materi\u00e1l).<\/p>\n

  <\/span>   <\/span>\"\[<\/p>\n","protected":false},"excerpt":{"rendered":"

Matematick\u00e1 interpretace elektromagnetick\u00e9 indukce vych\u00e1z\u00ed z Faradayova z\u00e1kona (indukovan\u00e9 nap\u011bt\u00ed je \u00fam\u011brn\u00e9 zm\u011bn\u011b magnetick\u00e9ho toku), Lenzova pravidla (sm\u011br indukovan\u00e9ho nap\u011bt\u00ed je proti zm\u011bn\u011b magnetick\u00e9ho toku) …. <\/p>\n","protected":false},"author":1,"featured_media":2515,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86],"tags":[88,72],"class_list":["post-4799","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-elektromagneticka-indukce","tag-matematika","tag-zakony"],"_links":{"self":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts\/4799","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4799"}],"version-history":[{"count":0,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts\/4799\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/media\/2515"}],"wp:attachment":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4799"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4799"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4799"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}