{"id":209578,"date":"2024-10-01T19:11:39","date_gmt":"2024-10-01T19:11:39","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/?p=209578"},"modified":"2024-10-01T19:11:39","modified_gmt":"2024-10-01T19:11:39","slug":"comment-trouver-le-champ-electrique-du-a-une-coque-spherique-chargee","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/fr\/comment-trouver-le-champ-electrique-du-a-une-coque-spherique-chargee\/","title":{"rendered":"Comment trouver le champ \u00e9lectrique d\u00fb \u00e0 une coque sph\u00e9rique charg\u00e9e ?"},"content":{"rendered":"<p class=\"sidekick\">Comment trouver le champ \u00e9lectrique d\u00fb \u00e0 une coque sph\u00e9rique charg\u00e9e? Apprenez les concepts cl\u00e9s et les \u00e9tapes pour calculer ce champ en physique thermique.<\/p>\n<h2>Comment trouver le champ \u00e9lectrique d\u00fb \u00e0 une coque sph\u00e9rique charg\u00e9e ?<\/h2>\n<p>En physique, le champ \u00e9lectrique d\u00fb \u00e0 une coque sph\u00e9rique charg\u00e9e est un concept cl\u00e9, en particulier dans les applications de l&rsquo;\u00e9lectrostatique. Cette situation peut \u00eatre analys\u00e9e gr\u00e2ce \u00e0 la loi de Gauss, l&rsquo;une des lois fondamentales de l&rsquo;\u00e9lectrostatique. Voici comment proc\u00e9der pour d\u00e9terminer ce champ \u00e9lectrique.<\/p>\n<h3>1. La loi de Gauss<\/h3>\n<p>La loi de Gauss pour le champ \u00e9lectrique est formul\u00e9e comme suit :<\/p>\n<p>\n\\[ \\oint_S \\vec{E} \\cdot d\\vec{A} = \\frac{Q_{\\text{enc}}}{\\epsilon_0} \\]\n<\/p>\n<p>o\u00f9 :<\/p>\n<ul>\n<li>\\( \\oint_S \\vec{E} \\cdot d\\vec{A} \\) est le flux du champ \u00e9lectrique \u00e0 travers une surface ferm\u00e9e \\( S \\).<\/li>\n<li>\\( Q_{\\text{enc}} \\) est la charge \u00e9lectrique totale enferm\u00e9e par la surface \\( S \\).<\/li>\n<li>\\( \\epsilon_0 \\) est la permittivit\u00e9 du vide.<\/li>\n<\/ul>\n<h3>2. Cas d&rsquo;une coque sph\u00e9rique charg\u00e9e<\/h3>\n<p>Supposons une coque sph\u00e9rique de rayon \\( R \\) uniform\u00e9ment charg\u00e9e de charge totale \\( Q \\). Nous devons d\u00e9terminer le champ \u00e9lectrique \u00e0 deux endroits : \u00e0 l&rsquo;ext\u00e9rieur de la coque et \u00e0 l&rsquo;int\u00e9rieur de la coque.<\/p>\n<h4>2.1. Champ \u00e9lectrique \u00e0 l&rsquo;ext\u00e9rieur de la coque (r &gt; R)<\/h4>\n<p>\nQuand \\( r > R \\), o\u00f9 \\( r \\) est la distance du centre de la sph\u00e8re \u00e0 un point d&rsquo;int\u00e9r\u00eat \u00e0 l&rsquo;ext\u00e9rieur de la coque, nous consid\u00e9rons une surface gaussienne sph\u00e9rique de rayon \\( r \\). Selon la loi de Gauss, avec une distribution sph\u00e9rique de la charge, le champ \u00e9lectrique \u00e0 l&rsquo;ext\u00e9rieur de la coque est comme si toute la charge \\( Q \\) \u00e9tait concentr\u00e9e en un point au centre :<\/p>\n<p>\n\\[ E \\cdot 4\\pi r^2 = \\frac{Q}{\\epsilon_0} \\]\n<\/p>\n<p>En simplifiant, on obtient :<\/p>\n<p>\n\\[ E = \\frac{Q}{4\\pi \\epsilon_0 r^2} \\]\n<\/p>\n<h4>2.2. Champ \u00e9lectrique \u00e0 l&rsquo;int\u00e9rieur de la coque (r &lt; R)<\/h4>\n<p>\nQuand \\( r < R \\), une surface gaussienne \u00e0 l'int\u00e9rieur de la coque sph\u00e9rique ne renferme aucune charge (puisque toute la charge est sur la coque elle-m\u00eame). Donc, selon la loi de Gauss :<\/p>\n<p>\n\\[ E \\cdot 4\\pi r^2 = 0 \\]\n<\/p>\n<p>Cela implique que le champ \u00e9lectrique \u00e0 l&rsquo;int\u00e9rieur de la coque est nul :<\/p>\n<p>\n\\[ E = 0 \\]\n<\/p>\n<h3>3. R\u00e9sum\u00e9<\/h3>\n<p>Pour une coque sph\u00e9rique charg\u00e9e :<\/p>\n<ol>\n<li>\u00c0 l&rsquo;ext\u00e9rieur de la coque (\\( r > R \\)), le champ \u00e9lectrique est \\( E = \\frac{Q}{4\\pi \\epsilon_0 r^2} \\).<\/li>\n<li>\u00c0 l&rsquo;int\u00e9rieur de la coque (\\( r < R \\)), le champ \u00e9lectrique est nul (\\( E = 0 \\)).<\/li>\n<\/ol>\n<p>Ce r\u00e9sultat montre comment le champ \u00e9lectrique varie en fonction de la position par rapport \u00e0 une coque sph\u00e9rique uniform\u00e9ment charg\u00e9e et illustre l&rsquo;\u00e9l\u00e9gance et la puissance de la loi de Gauss en \u00e9lectrostatique.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Comment trouver le champ \u00e9lectrique d\u00fb \u00e0 une coque sph\u00e9rique charg\u00e9e? Apprenez les concepts cl\u00e9s et les \u00e9tapes pour calculer ce champ en physique thermique.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_generate-full-width-content":"","footnotes":""},"categories":[98],"tags":[],"class_list":["post-209578","post","type-post","status-publish","format-standard","hentry","category-des-questions","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>Comment trouver le champ \u00e9lectrique d\u00fb \u00e0 une coque sph\u00e9rique charg\u00e9e ?<\/title>\n<meta name=\"description\" content=\"Comment trouver le champ \u00e9lectrique d\u00fb \u00e0 une coque sph\u00e9rique charg\u00e9e? 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