{"id":34783,"date":"2021-08-31T13:00:21","date_gmt":"2021-08-31T13:00:21","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34783"},"modified":"2025-09-21T00:06:57","modified_gmt":"2025-09-21T00:06:57","slug":"lex-coulombii-et-vis-electrostatica","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/lex-coulombii-et-vis-electrostatica\/","title":{"rendered":"Lex Coulombii et Vis Electrostatica"},"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>Lex Coulombii et Vis Electrostatica<\/h1>\n<p style=\"text-align:center;\">\n\u00abLex Coulombii et Vis Electrostatica\u00bb non solum intellegentiam nostram de viribus electricis auxit, sed etiam narrationes inopinatas genuit. Benjamin Franklin, in experimento quo pavonem electricitate sternere et coquere conatus est, ipse subiectum probationis factus est: displosio eum perturbavit et capillos erexit, quasi lineas campi electrici in vita ostendens. Nunc autem nostrum est tempus vires electricas investigare.\n<\/p>\n<p style=\"text-align:center;\"><strong>Proposita discendi:<\/strong><br \/>\nAd finem huius lectionis discipulus poterit<\/p>\n<ol>\n<li><strong>Modellari<\/strong> phaenomena electrica utens principio superpositionis ad vim resultantem in onere probando computandam.<\/li>\n<li><strong>Simplificare<\/strong> studium virium electricarum ad casum electrostaticum restringendo.<\/li>\n<li><strong>Applicare<\/strong> Legem Coulombii ad vim inter duo onera in variis condicionibus determinandam.<\/li>\n<li><strong>Analyzare<\/strong> systemata circa fontem oneris posita per formulam simplificatam Legis Coulombii.<\/li>\n<li><strong>Solvere<\/strong> problemata practica ad distributiones onerum pertinentia.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Principium superpositionis<\/a><br \/>\n<a href=\"#2\">Simplificatio electrostatica<\/a><br \/>\n<a href=\"#3\">Lex Coulombii<\/a><br \/>\n<a href=\"#4\">Lex Coulombii pro systematibus circa fontem onerum<\/a><br \/>\n<a href=\"#5\">Exercitia<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/RV3Uzorlkr4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p>Nunc tempus est haec phaenomena mathematicis modis exprimere atque ad hoc introducemus <strong>Legem Coulombii.<\/strong> Sed antea necesse est nonnulla explicare, haec sunt: Principium superpositionis et simplificatio electrostatica.<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Principium superpositionis<\/h2>\n<p>Problema fundamentale electrodynamicae est determinare vim quam \u00abnubes\u00bb onerum electricorum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1<\/span><\/span>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_2<\/span><\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">\\cdots<\/span> exercent super onus probationis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span>,<\/span> cum positio uniuscuiusque earum functio temporis nota sit. Generaliter tam fontes onerum quam onus probationis in motu relativo sunt.<\/p>\n<p>Solutio huius problematis per principium superpositionis facilior fit, quod nobis dicit interactionem oneris probationis cum aliqua fonte omnino independentem esse ab interactione cum ceteris fontibus onerum. Hoc significat semper possibile esse determinare vim <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_1<\/span><\/span> quam confert onus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1<\/span>,<\/span> vim <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_2<\/span><\/span> quam confert <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_2<\/span><\/span> et sic deinceps, ut tandem addamus et vim totam obtineamus<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{tot} = \\displaystyle \\sum_{i}\\vec{F}_i<\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Simplificatio electrostatica<\/h2>\n<p>Si tantum vires addendae sunt, aliquis dicere posset satis esse indicare aequationem quae vim describit quam unaquaeque fons oneris exercet super onus probationis et quaestionem solutam fore; tamen res non tam simplex est. Quaestio est quod vis non solum a distantia et magnitudine onerum pendet, sed etiam a velocitate et acceleratione relativa uniuscuiusque particulae. Praeterea \u00abinformatio electrica\u00bb de mutationibus positionis, velocitatis et accelerationis cuiusque particulae celeritate lucis propagatur, unde certo tempore ad onus probationis pervenit et effectum suum mutat.<\/p>\n<p>Itaque, ut studium nostrum nunc simplificemus, nos ad casum <strong>electrostaticum<\/strong> restringemus, id est: omnes fontes onerum stabiles manebunt, solum onus probationis moveri poterit; et hoc in contextu <strong>Lex Coulombii<\/strong> emergit.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Lex Coulombii<\/h2>\n<p>Ponamus nos habere onus probationis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span>.<\/span> cum positione <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span><\/span> et fontem oneris <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> cum positione <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}^\\prime<\/span>.<\/span> Quae erit vis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{q \\to q_0}(\\vec{r})<\/span><\/span> fontis oneris super onus probationis? Responsio huius quaestionis datur per <strong>Legem Coulombii,<\/strong> quae formula exprimitur:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{q \\to q_0} (\\vec{r}) =\\displaystyle \\frac{1}{4\\pi \\epsilon_0}  \\frac{q  q_0 }{\\|\\vec{r} - \\vec{r}^\\prime \\|^2} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|}<\/span><\/span><\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-amszqS6iLRk\/YSwCV4TCIZI\/AAAAAAAAFec\/XoTDZm0i-6oPZY4KuGv0xOEbrsYCfJM4wCLcBGAsYHQ\/s0\/fuerzaelectrica.PNG\" width=\"492\" height=\"390\" alt=\"Vis Electrica\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-amszqS6iLRk\/YSwCV4TCIZI\/AAAAAAAAFec\/XoTDZm0i-6oPZY4KuGv0xOEbrsYCfJM4wCLcBGAsYHQ\/s0\/fuerzaelectrica.PNG\" width=\"492\" height=\"390\" alt=\"Vis Electrica\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p>Lex Coulombii non solum legem signorum pro vi electrostatica comprehendit, sed etiam statuit vim inter onera electrica inverse proportionalem esse quadrato distantiae quae ea separat.<\/p>\n<p>Constans <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon_0<\/span><\/span> appellatur <strong>constans permissivitatis electricae vacui.<\/strong> Valor eius in systemate internationali est<\/p>\n<p>,<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\epsilon_0 = 8,85 \\cdot 10^{-12} \\left[ \\frac{C^2}{N\\cdot m^2}\\right] <\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Lex Coulombii pro systematibus circa fontem onerum<\/h2>\n<p><strong>Lex Coulombii<\/strong> simplicius exprimi potest si spectatorem super fontem onerum ponamus, id est: faciendo <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}^\\prime = \\vec{0}<\/span>.<\/span> Hoc modo habebitur<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{F}_{q \\to q_0} (\\vec{r}) = \\frac{1}{4\\pi \\epsilon_0}  \\frac{q  q_0 }{\\|\\vec{r}\\|^2}   \\frac{\\vec{r} }{\\|\\vec{r} \\|} = \\frac{1}{4\\pi \\epsilon_0}  \\frac{q   q_0 }{\\|\\vec{r}\\|^2} \\hat{r}<\/span><\/span><\/p>\n<p>Ubi <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{r}=\\vec{r}\/\\|\\vec{r}\\|<\/span><\/span> est vector unitarius qui a fonte ad onus probationis dirigi solet.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>Exercitia<\/h2>\n<ol>\n<li>Duodecim onera punctalia aequalis magnitudinis <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> in angulis polygonii regularis duodecim laterum ponuntur (sicut numeri horologii). Quae erit vis neta super onus punctale <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> in centro positum?<\/li>\n<li>Unum ex duodecim oneribus exercitii prioris removetur, ponamus illud esse quod hora duodecima esset (si ut horologium imaginamus). Quam vim sentiet nunc onus punctale <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span>?<\/li>\n<li>Extendite rationem duorum exercitiorum priorum, sed nunc ad distributionem <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> fontium onerum dispositam super polygono regulari <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> cum onere probationis in centro.<\/li>\n<li>Tria onera punctalia habentur: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1=+3[nC]<\/span><\/span> cum positione <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(0;0)[mm]<\/span>,<\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_2=-5[nC]<\/span><\/span> cum positione <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(0,56;0)[mm]<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_3=+7[nC]<\/span><\/span> cum positione <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1;1)[mm]<\/span>.<\/span> Computetur vis tota super onus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_3<\/span>.<\/span><\/li>\n<li>In axe invenitur onus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1 = 3[C]<\/span>,<\/span> et ad distantiam <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">40[mm]<\/span><\/span> aliud onus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_2 = 7[C]<\/span>.<\/span> Si inter haec duo onera tertium ponitur ita ut summa virium super illud sit nulla, quae erit distantia inter hoc tertium onus et alia duo?<\/li>\n<li>Duae parvae sphaerae cupreae, quarum unaquaeque massam <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0,040[kg]<\/span><\/span> habet, distantia <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2,0[m]<\/span><\/span> separatae ponuntur. Considerantes massam molarem cupri esse <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">63,5[g\/mol]<\/span><\/span> et numerum atomicum 20, responde quaestionibus sequentibus:\n<ol>\n<li type=\"a\">Quot electrones habet unaquaeque sphaera?<\/li>\n<li type=\"a\">Quot electrones necesse est movere ab una sphaera ad alteram ut vis attractionis inter sphaeras sit circiter <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">10^4[N]<\/span>.<\/span><\/li>\n<li type=\"a\">Quae fractio electronum sphaerarum id repraesentat?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/jxO34PM91Io\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n<br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/EBOxmKPQe9U\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lex Coulombii et Vis Electrostatica \u00abLex Coulombii et Vis Electrostatica\u00bb non solum intellegentiam nostram de viribus electricis auxit, sed etiam narrationes inopinatas genuit. Benjamin Franklin, in experimento quo pavonem electricitate sternere et coquere conatus est, ipse subiectum probationis factus est: displosio eum perturbavit et capillos erexit, quasi lineas campi electrici in vita ostendens. Nunc autem [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30950,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":2,"footnotes":""},"categories":[1256,1250],"tags":[],"class_list":["post-34783","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>Lex Coulombii et Vis Electrostatica - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Lex Coulombii vim electrostaticam inter duo onera describit: proportionalem producto onerum et inverse quadratui distantiae.\" \/>\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\/lex-coulombii-et-vis-electrostatica\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lex Coulombii et Vis Electrostatica\" \/>\n<meta property=\"og:description\" content=\"Lex Coulombii vim electrostaticam inter duo onera describit: proportionalem producto onerum et inverse quadratui distantiae.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/la\/lex-coulombii-et-vis-electrostatica\/\" \/>\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=\"2021-08-31T13:00:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-21T00:06:57+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/electrostatica-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Lex Coulombii et Vis Electrostatica\" \/>\n<meta name=\"twitter:description\" content=\"Lex Coulombii vim electrostaticam inter duo onera describit: proportionalem producto onerum et inverse quadratui distantiae.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/electrostatica.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\\\/lex-coulombii-et-vis-electrostatica\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/lex-coulombii-et-vis-electrostatica\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Lex Coulombii et Vis Electrostatica\",\"datePublished\":\"2021-08-31T13:00:21+00:00\",\"dateModified\":\"2025-09-21T00:06:57+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/lex-coulombii-et-vis-electrostatica\\\/\"},\"wordCount\":861,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/lex-coulombii-et-vis-electrostatica\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2025\\\/01\\\/electrostatica.jpg\",\"articleSection\":[\"Electromagnetismus\",\"Physica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/lex-coulombii-et-vis-electrostatica\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/lex-coulombii-et-vis-electrostatica\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/lex-coulombii-et-vis-electrostatica\\\/\",\"name\":\"Lex Coulombii et Vis Electrostatica - 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