{"id":80436,"date":"2024-01-14T13:04:33","date_gmt":"2024-01-14T13:04:33","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/formula-da-lei-de-gauss-equacao-calculo\/"},"modified":"2024-01-20T09:47:12","modified_gmt":"2024-01-20T09:47:12","slug":"formula-da-lei-de-gauss-equacao-calculo","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-da-lei-de-gauss-equacao-calculo\/","title":{"rendered":"F\u00f3rmula da Lei de Gauss &#8211; Equa\u00e7\u00e3o | C\u00e1lculo"},"content":{"rendered":"<h2>Lei de Gauss: Uma Vis\u00e3o Fundamental na Eletromagnetismo<\/h2>\n<p>A Lei de Gauss, uma pedra angular do eletromagnetismo, desempenha um papel crucial na compreens\u00e3o da rela\u00e7\u00e3o entre a distribui\u00e7\u00e3o de carga el\u00e9trica e o campo el\u00e9trico resultante. Esta lei, tamb\u00e9m conhecida como o teorema do fluxo de Gauss, \u00e9 particularmente \u00fatil para analisar situa\u00e7\u00f5es com distribui\u00e7\u00f5es de carga de alta simetria.<\/p>\n<h2>Conceito de Fluxo El\u00e9trico<\/h2>\n<p>O fluxo el\u00e9trico, representado por \u03a6, \u00e9 uma medida fundamental na Lei de Gauss. Ele descreve o campo el\u00e9trico E que atravessa uma determinada \u00e1rea A. Matematicamente, \u00e9 expresso como \u03a6 = E x A para uma \u00e1rea perpendicular ao vetor E. Quando a \u00e1rea n\u00e3o \u00e9 perpendicular, o fluxo el\u00e9trico \u00e9 definido como \u03a6 = E x A x cos\u03c6.<\/p>\n<h2>Lei de Gauss em Sua Forma Integral<\/h2>\n<p>A Lei de Gauss em sua forma integral estabelece uma rela\u00e7\u00e3o entre a carga el\u00e9trica encerrada por uma superf\u00edcie fechada (superf\u00edcie gaussiana) e o fluxo el\u00e9trico total atrav\u00e9s dessa superf\u00edcie. Esta rela\u00e7\u00e3o \u00e9 expressa pela equa\u00e7\u00e3o \u03a6<sub>E<\/sub> = Q\/\u03b5<sub>0<\/sub>, onde Q \u00e9 a carga el\u00e9trica l\u00edquida dentro da superf\u00edcie e \u03b5<sub>0<\/sub> \u00e9 a constante de permissividade do espa\u00e7o livre.<\/p>\n<h2>Fluxo El\u00e9trico em Campos N\u00e3o Uniformes<\/h2>\n<p>Em situa\u00e7\u00f5es onde o campo el\u00e9trico E n\u00e3o \u00e9 uniforme ou a superf\u00edcie \u00e9 curva, o c\u00e1lculo do fluxo el\u00e9trico se torna mais complexo. Neste caso, o fluxo el\u00e9trico d\u03a6<sub>E<\/sub> atrav\u00e9s de uma pequena \u00e1rea dA \u00e9 dado por d\u03a6<sub>E<\/sub> = E x dA. Calculamos o fluxo el\u00e9trico atrav\u00e9s de cada elemento e integramos os resultados para obter o fluxo total.<\/p>\n<h2>Forma Diferencial da Lei de Gauss<\/h2>\n<p>A Lei de Gauss tamb\u00e9m pode ser expressa em sua forma diferencial, que relaciona a diverg\u00eancia do campo el\u00e9trico com a densidade local de carga. Conhecida como teorema da diverg\u00eancia ou teorema de Gauss-Ostrogradsky, esta forma \u00e9 particularmente \u00fatil para an\u00e1lises detalhadas de campos el\u00e9tricos.<\/p>\n<h2>Aplica\u00e7\u00f5es e Analogias<\/h2>\n<p>A Lei de Gauss \u00e9 frequentemente utilizada para determinar campos el\u00e9tricos em situa\u00e7\u00f5es com distribui\u00e7\u00f5es de carga sim\u00e9tricas. \u00c9 an\u00e1loga \u00e0 Lei de Amp\u00e8re no magnetismo e constitui uma das quatro equa\u00e7\u00f5es de Maxwell, fundamentais para a eletrodin\u00e2mica cl\u00e1ssica. A unidade de carga el\u00e9trica no Sistema Internacional de Unidades (SI) \u00e9 o Coulomb (C), definido como a quantidade de eletricidade transportada em um segundo por uma corrente de um ampere.<\/p>\n<h2>Conclus\u00e3o<\/h2>\n<p>A Lei de Gauss \u00e9 um princ\u00edpio essencial na f\u00edsica, proporcionando uma compreens\u00e3o profunda das rela\u00e7\u00f5es entre carga el\u00e9trica e campo el\u00e9trico. Sua aplicabilidade em situa\u00e7\u00f5es com alta simetria torna-a uma ferramenta poderosa no estudo do eletromagnetismo.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.electricity-magnetism.org\/wp-content\/uploads\/2022\/02\/Gauss-law-equation-formula.png\" alt=\"\" \/><\/p>\n<div style=\"text-align: center; font-size: 20px;\">\n    <a href=\"https:\/\/www.electricity-magnetism.org\/electrostatics\/gausss-law\/gausss-law-formula-equation\/\">Original Article<\/a>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Na sua forma integral, a lei de Gauss relaciona a carga encerrada por uma superf\u00edcie fechada com o fluxo total atrav\u00e9s dessa superf\u00edcie. F\u00f3rmula da Lei de Gauss &#8211; Equa\u00e7\u00e3o<\/p>\n","protected":false},"author":1,"featured_media":2141,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_generate-full-width-content":"","footnotes":""},"categories":[14],"tags":[],"class_list":["post-80436","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nao-categorizado","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>F\u00f3rmula da Lei de Gauss - Equa\u00e7\u00e3o | C\u00e1lculo<\/title>\n<meta name=\"description\" content=\"Na sua forma integral, a lei de Gauss relaciona a carga encerrada por uma superf\u00edcie fechada com o fluxo total atrav\u00e9s dessa superf\u00edcie. 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