{"id":34798,"date":"2021-09-21T13:00:34","date_gmt":"2021-09-21T13:00:34","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34798"},"modified":"2025-09-21T02:17:38","modified_gmt":"2025-09-21T02:17:38","slug":"conceptus-campi-electrici","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/conceptus-campi-electrici\/","title":{"rendered":"Conceptus campi electrici"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\ttext-align:center;\n\t}\n<\/style>\n<h1>Conceptus campi electrici<\/h1>\n<p style=\"text-align:center;\"><em>Saeculo XIX, Michael Faraday, unus ex maximis experimentatoribus in campo electricitatis, more peculiari utebatur: officinam suam implebat filis, sphaeris onustis et parvis vasis liquidis conductoribus. Famosa narratio tradit eum, in cupiditate sua \u00ablineas virium\u00bb circum onus electricum visibiliter ostendendi, limaturas ferri per totam officinam dispersisse, pavimentum relinquentem vestigiis quae artem modernam imitari videbantur. Collegae eius, perplexi, putaverunt eum mentem amisisse, sed Faraday unum e conceptibus maxime revolutionariis delineabat: campum electricum. In hoc articulo explorabimus quomodo hae ideae, ex ingenio et experimentis ortae, nobis sinant invisibiles interactiones, quae electricitatem regunt, describere et intellegere. Si umquam quaesivisti quomodo res intangibiles videri possint, hic cursus tibi destinatur.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Proposita Discendi:<\/strong><br \/>\nAd finem huius lectionis discipulus poterit\n<\/p>\n<ol>\n<li><strong>Intellegere<\/strong> conceptum campi electrici eiusque relationem cum vi electrica per Legem Coulombianam.<\/li>\n<li><strong>Applicare<\/strong> definitionem campi electrici ad solvenda problemata ad onera punctalia pertinentia.<\/li>\n<li><strong>Analyzare<\/strong> principium superpositionis in distributionibus discretis et continuis onerum ad campos electricos computandos.<\/li>\n<li><strong>Aestimare<\/strong> integrationem distributionum linearum, superficialium et volumetricarum ad campos electricos in configurationibus complexis determinandos.<\/li>\n<li><strong>Solvere<\/strong> exercitationes practicas quae includunt configurationes vectis onustae, anuli onusti et plani infiniti onusti.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Quid est campus electricus?<\/a><br \/>\n<a href=\"#2\">Campus electricus et distributiones onerum<\/a><br \/>\n<a href=\"#3\">Exercitationes<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KWwRfJ9ZRrA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Quid est campus electricus?<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=191s\" target=\"_blank\" rel=\"noopener\"><strong>Cum fontem oneris<\/strong><\/a> in aliquo spatii loco ponimus, praesentiam eius sentire possumus utendo onere probatorio propter <strong>vim electricam<\/strong> quam iste sentit ob praesentiam. Hanc vim per Legem Coulombianam investigamus. Hoc innixi dicimus fontem oneris \u00abspatium inundare\u00bb quadam proprietate, Campo Electrico, qui vim electricam producere responsalis est.<\/p>\n<p>Ad campum electricum oneris <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> in certo loco <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> spatii metiendum, necesse est onus probationis <span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span> ibi collocare. Campus electricus describetur ut quantitas vis electricae quam onus probationis <span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span> sentit per unitatem oneris.<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{E}_q(\\vec{r}) = \\displaystyle \\frac{\\vec{F}_{q\\to q_0}(\\vec{r})}{q_0}<\/span>\n<p>At vero cum hoc modo procedimus, neglegimus quod etiam onus probationis proprium campum electricum habere debet, qui cum campo fontis onerum superponetur. Ad hanc quaestionem solvendi, de campo electrico loquimur per limitem:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\vec{E}_q(\\vec{r}) = \\lim_{q_0 \\to 0} \\frac{\\vec{F}_{q\\to q_0}(\\vec{r})}{q_0}<\/span>\n<p>Definitone per limitem utens, curamus ut campus oneris probationis <span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span> mensurationibus campi oneris <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> non intersitet. Nunc, Legem Coulombianam recolentes, campus electricus particulae onustae <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> ita se habet:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\vec{E}_q(\\vec{r}) = \\lim_{q_0 \\to 0} \\frac{1}{q_0} \\frac{1}{4\\pi \\epsilon_0} \\frac{qq_0}{\\|\\vec{r} -\\vec{r}^\\prime\\|^2} \\frac{\\vec{r} -\\vec{r}^\\prime}{\\|\\vec{r} -\\vec{r}^\\prime\\|} = \\frac{q}{4\\pi\\epsilon_0} \\frac{\\vec{r} -\\vec{r}^\\prime}{\\|\\vec{r} -\\vec{r}^\\prime\\|^3} <\/span>\n<p>Et, ex hoc habetur quod<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{F}_{q\\to q_0}(\\vec{r}) = q_0 \\vec{E}_q(\\vec{r}) <\/span>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Campus electricus et distributiones onerum<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=565s\" target=\"_blank\" rel=\"noopener\"><strong>Quoniam campus electricus<\/strong><\/a> secundum vim investigatur, et hic principiis superpositionis satisfacit, possumus campos diversarum distributionum onerum examinare.<\/p>\n<h3>Distributiones discretae<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=587s\" target=\"_blank\" rel=\"noopener\"><strong>Consideremus distributionem <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> onerum discretorum<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">q_1, q_2, \\cdots, q_n<\/span> cum positionibus <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}^\\prime_1, \\vec{r}^\\prime_2, \\cdots, \\vec{r}^\\prime_n.<\/span> Si volumus campum earum in aliquo loco <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> spatii computare, tum habebitur:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\vec{E}_q(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\sum_{i=1}^n q_i \\frac{\\vec{r} -\\vec{r}_i^\\prime}{\\|\\vec{r} -\\vec{r}_i^\\prime\\|^3} <\/span>\n<p>Id est, summa omnium camporum singularium.<\/p>\n<h3>Distributiones continuae<\/h3>\n<p>Tria genera distributionum continuarum onerum exstant, unumquodque numero parametronum necessariorum ad dispositionem spatialem describendam associatum. Hae sunt distributiones lineares, superficiales et volumetricae.<\/p>\n<h4>Distributio linearis<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=688s\" target=\"_blank\" rel=\"noopener\"><strong>In distributione lineari oneris,<\/strong><\/a> unumquodque elementum lineae corporis onusti densitatem linearem oneris habet <span class=\"katex-eq\" data-katex-display=\"false\">\\lambda(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dl<\/span>, ita ut elementum campi electrici sit huiusmodi.<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">d\\vec{E}(\\vec{r}) =\\displaystyle \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\lambda(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dl<\/span>\n<p>Deinde, si hanc expressionem integramus, habetur:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\int_{\\mathcal{C}} \\lambda(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dl<\/span>\n<p>Ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}<\/span> est repraesentatio parametrica curvae quae figuram corporis onusti describit.<\/p>\n<h4>Distributio superficialis<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=899s\" target=\"_blank\" rel=\"noopener\"><strong>In distributione superficiali oneris<\/strong><\/a>, unumquodque elementum superficiei corporis onusti densitatem superficialem oneris habet <span class=\"katex-eq\" data-katex-display=\"false\">\\sigma(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dS<\/span>, ita ut elementum campi electrici huiusmodi sit.<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle d\\vec{E}(\\vec{r}) = \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\sigma(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dS<\/span>\n<p>Deinde, si hanc expressionem integramus, habetur:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\iint_{\\mathcal{A}} \\sigma(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dS<\/span>\n<p>Ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span> est repraesentatio parametrica superficiei quae figuram corporis onusti describit.<\/p>\n<h4>Distributio volumetrica<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=1054s\" target=\"_blank\" rel=\"noopener\"><strong>In distributione volumetrica oneris<\/strong><\/a>, unumquodque elementum voluminis corporis onusti densitatem volumetricam oneris habet <span class=\"katex-eq\" data-katex-display=\"false\">\\rho(\\vec{r}_i^\\prime)=dq(\\vec{r}_i^\\prime)\/dV<\/span>, ita ut elementum campi electrici huiusmodi sit.<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle d\\vec{E}(\\vec{r}^\\prime) = \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\rho(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dV<\/span>\n<p>Deinde, si hanc expressionem integramus, habetur:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\iiint_{\\mathcal{V}} \\rho(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dV<\/span>\n<p>Ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{V}<\/span> est repraesentatio parametrica voluminis quae figuram corporis onusti describit.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Exercitationes:<\/h2>\n<h3>Barra onusta<\/h3>\n<p>Consideretur barra longitudinis <span class=\"katex-eq\" data-katex-display=\"false\">L<\/span> uniformiter onusta cum onere <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> et verticaliter posita. Determina campum electricum barrae ad distantiam horizontalem <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> a centro barrae.<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/PEi3xjHDyxM\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h3>Anulus onustus<\/h3>\n<p>Consideretur anulus radii <span class=\"katex-eq\" data-katex-display=\"false\">R<\/span> uniformiter onustus cum onere <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> in plano xy positus. Determina campum electricum statim ad altitudinem <span class=\"katex-eq\" data-katex-display=\"false\">z<\/span> a centro anuli.<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/kPVAhlzvgKA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h3>Planum infinitum onustum<\/h3>\n<p>Consideretur planum infinitum uniformiter onustum cum densitate superficiali oneris <span class=\"katex-eq\" data-katex-display=\"false\">\\sigma<\/span>. Determina campum electricum ad distantiam <span class=\"katex-eq\" data-katex-display=\"false\">L<\/span> a plano.<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/IQeDWxVT7eM\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Conceptus campi electrici Saeculo XIX, Michael Faraday, unus ex maximis experimentatoribus in campo electricitatis, more peculiari utebatur: officinam suam implebat filis, sphaeris onustis et parvis vasis liquidis conductoribus. Famosa narratio tradit eum, in cupiditate sua \u00ablineas virium\u00bb circum onus electricum visibiliter ostendendi, limaturas ferri per totam officinam dispersisse, pavimentum relinquentem vestigiis quae artem modernam imitari [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30980,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":15,"footnotes":""},"categories":[1256,1250],"tags":[],"class_list":["post-34798","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electromagnetismus","category-physica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Conceptus campi electrici - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Campus electricus est regio ubi onus vim in alia onera generat, quae per intensitatem et directionem in unoquoque puncto describitur.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/la\/conceptus-campi-electrici\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Conceptus campi electrici\" \/>\n<meta property=\"og:description\" content=\"Campus electricus est regio ubi onus vim in alia onera generat, quae per intensitatem et directionem in unoquoque puncto describitur.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/la\/conceptus-campi-electrici\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-21T13:00:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-21T02:17:38+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/campoelectrico-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Conceptus campi electrici\" \/>\n<meta name=\"twitter:description\" content=\"Campus electricus est regio ubi onus vim in alia onera generat, quae per intensitatem et directionem in unoquoque puncto describitur.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/campoelectrico.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/conceptus-campi-electrici\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/conceptus-campi-electrici\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Conceptus campi electrici\",\"datePublished\":\"2021-09-21T13:00:34+00:00\",\"dateModified\":\"2025-09-21T02:17:38+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/conceptus-campi-electrici\\\/\"},\"wordCount\":1083,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/conceptus-campi-electrici\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2025\\\/01\\\/campoelectrico.jpg\",\"articleSection\":[\"Electromagnetismus\",\"Physica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/conceptus-campi-electrici\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/conceptus-campi-electrici\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/conceptus-campi-electrici\\\/\",\"name\":\"Conceptus campi electrici - 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