{"id":1620,"date":"2026-09-08T08:07:34","date_gmt":"2026-09-08T08:07:34","guid":{"rendered":"https:\/\/maroczain.com\/scolaire.maroczain.com\/?page_id=1620"},"modified":"2026-09-08T08:07:34","modified_gmt":"2026-09-08T08:07:34","slug":"electromagnetisme-avance-cpge","status":"publish","type":"page","link":"https:\/\/maroczain.com\/scolaire.maroczain.com\/electromagnetisme-avance-cpge\/","title":{"rendered":"\u00c9lectromagn\u00e9tisme avanc\u00e9 CPGE."},"content":{"rendered":"\n&#8220;`html\n<div id=\"mza-electromagnetisme-avance-cpge\">\n\n<style>\n#mza-electromagnetisme-avance-cpge,\n#mza-electromagnetisme-avance-cpge *{box-sizing:border-box}\n\n#mza-electromagnetisme-avance-cpge{\n --navy:#06172c;\n --navy2:#0d416d;\n --gold:#c99a36;\n --gold2:#efd68c;\n --paper:#f5f6f8;\n --white:#fff;\n --text:#18283a;\n --muted:#687789;\n --line:#dfe5eb;\n font-family:Arial,Helvetica,sans-serif;\n background:var(--paper);\n color:var(--text);\n overflow:hidden\n}\n\n#mza-electromagnetisme-avance-cpge a{text-decoration:none;color:inherit}\n#mza-electromagnetisme-avance-cpge .wrap{max-width:1200px;margin:auto;padding:0 24px}\n#mza-electromagnetisme-avance-cpge section{padding:68px 0}\n\n#mza-electromagnetisme-avance-cpge .hero{\n color:#fff;\n padding:72px 0;\n background:\n radial-gradient(circle at 84% 15%,rgba(213,169,68,.28),transparent 28%),\n linear-gradient(135deg,#041224,#082b4c 65%,#10517e)\n}\n\n#mza-electromagnetisme-avance-cpge .badge{\n display:inline-block;\n padding:8px 13px;\n border-radius:999px;\n border:1px solid rgba(239,214,140,.4);\n color:var(--gold2);\n font-size:11px;\n font-weight:900;\n letter-spacing:1.3px\n}\n\n#mza-electromagnetisme-avance-cpge h1{\n font:500 clamp(42px,7vw,72px)\/1 Georgia,serif;\n margin:17px 0;\n color:#fff\n}\n\n#mza-electromagnetisme-avance-cpge .lead{\n max-width:900px;\n color:#d5e1ea;\n font-size:18px;\n line-height:1.75\n}\n\n#mza-electromagnetisme-avance-cpge .actions{\n display:flex;\n gap:9px;\n flex-wrap:wrap;\n margin-top:26px\n}\n\n#mza-electromagnetisme-avance-cpge .btn{\n min-height:47px;\n padding:0 18px;\n border:none;\n border-radius:10px;\n display:inline-flex;\n align-items:center;\n justify-content:center;\n cursor:pointer;\n font-size:12px;\n font-weight:900\n}\n\n#mza-electromagnetisme-avance-cpge .gold{\n background:linear-gradient(135deg,#bd892b,#efd483);\n color:#142238\n}\n\n#mza-electromagnetisme-avance-cpge .glass{\n background:rgba(255,255,255,.08);\n border:1px solid rgba(255,255,255,.18);\n color:#fff\n}\n\n#mza-electromagnetisme-avance-cpge .head{\n max-width:880px;\n margin-bottom:32px\n}\n\n#mza-electromagnetisme-avance-cpge .kicker{\n color:#987023;\n font-size:11px;\n font-weight:900;\n letter-spacing:1.3px\n}\n\n#mza-electromagnetisme-avance-cpge h2{\n color:var(--navy);\n font:500 clamp(31px,4vw,48px)\/1.1 Georgia,serif;\n margin:8px 0 11px\n}\n\n#mza-electromagnetisme-avance-cpge .head p{\n color:var(--muted);\n line-height:1.7\n}\n\n#mza-electromagnetisme-avance-cpge .grid{\n display:grid;\n grid-template-columns:repeat(2,1fr);\n gap:16px\n}\n\n#mza-electromagnetisme-avance-cpge .grid3{\n display:grid;\n grid-template-columns:repeat(3,1fr);\n gap:16px\n}\n\n#mza-electromagnetisme-avance-cpge .card{\n background:#fff;\n border:1px solid var(--line);\n border-radius:19px;\n padding:23px\n}\n\n#mza-electromagnetisme-avance-cpge .card h3{\n color:var(--navy);\n margin:0 0 10px;\n font-size:20px\n}\n\n#mza-electromagnetisme-avance-cpge .card p,\n#mza-electromagnetisme-avance-cpge .card li{\n color:var(--muted);\n line-height:1.7\n}\n\n#mza-electromagnetisme-avance-cpge .formula{\n margin:14px 0;\n padding:15px;\n border-left:4px solid var(--gold);\n background:#f8f6ef;\n border-radius:0 12px 12px 0;\n font-family:Georgia,serif;\n color:#213349;\n line-height:1.75\n}\n\n#mza-electromagnetisme-avance-cpge .tip{\n margin-top:14px;\n padding:13px;\n border-radius:11px;\n background:#eef3f7;\n color:#40546a;\n font-size:13px;\n line-height:1.6\n}\n\n#mza-electromagnetisme-avance-cpge .dark{\n background:var(--navy);\n color:#fff\n}\n\n#mza-electromagnetisme-avance-cpge .dark h2{color:#fff}\n#mza-electromagnetisme-avance-cpge .dark .head p{color:#c6d4df}\n\n#mza-electromagnetisme-avance-cpge .method{\n display:grid;\n grid-template-columns:repeat(6,1fr);\n gap:10px\n}\n\n#mza-electromagnetisme-avance-cpge .method div{\n padding:20px 10px;\n text-align:center;\n border-radius:14px;\n background:rgba(255,255,255,.07);\n border:1px solid rgba(255,255,255,.1)\n}\n\n#mza-electromagnetisme-avance-cpge .method b{\n display:block;\n color:var(--gold2);\n font-size:23px;\n margin-bottom:7px\n}\n\n#mza-electromagnetisme-avance-cpge .method span{\n font-size:10px;\n font-weight:900\n}\n\n#mza-electromagnetisme-avance-cpge .exercise{\n background:#fff;\n border:1px solid var(--line);\n border-radius:18px;\n padding:22px;\n margin-bottom:14px\n}\n\n#mza-electromagnetisme-avance-cpge .exercise h3{\n color:var(--navy);\n margin:0 0 10px\n}\n\n#mza-electromagnetisme-avance-cpge .level{\n display:inline-block;\n padding:6px 9px;\n margin-bottom:10px;\n border-radius:999px;\n background:#f1eee5;\n color:#7b5b1d;\n font-size:10px;\n font-weight:900\n}\n\n#mza-electromagnetisme-avance-cpge .exercise p{\n color:var(--muted);\n line-height:1.7\n}\n\n#mza-electromagnetisme-avance-cpge .hint{\n display:none;\n margin-top:12px;\n padding:15px;\n border-radius:12px;\n background:#eef3f7;\n color:#425469;\n line-height:1.65\n}\n\n#mza-electromagnetisme-avance-cpge .qcm{\n background:#fff;\n border:1px solid var(--line);\n border-radius:23px;\n padding:28px\n}\n\n#mza-electromagnetisme-avance-cpge .question{\n padding:20px;\n margin:15px 0;\n background:#f7f8fa;\n border-radius:14px\n}\n\n#mza-electromagnetisme-avance-cpge .question strong{\n display:block;\n color:var(--navy);\n margin-bottom:12px\n}\n\n#mza-electromagnetisme-avance-cpge label{\n display:block;\n padding:8px 0;\n color:#526174;\n cursor:pointer\n}\n\n#mza-electromagnetisme-avance-cpge #emResult{\n display:none;\n margin-top:18px;\n padding:20px;\n border-radius:14px;\n background:var(--navy);\n color:#fff\n}\n\n#mza-electromagnetisme-avance-cpge .cta{\n text-align:center;\n padding:50px 24px;\n border-radius:25px;\n background:linear-gradient(135deg,#06172c,#0d416d);\n color:#fff\n}\n\n#mza-electromagnetisme-avance-cpge .cta h2{color:#fff}\n\n#mza-electromagnetisme-avance-cpge .cta p{\n max-width:760px;\n margin:0 auto 22px;\n color:#cfdae4;\n line-height:1.7\n}\n\n@media(max-width:900px){\n #mza-electromagnetisme-avance-cpge .grid,\n #mza-electromagnetisme-avance-cpge .grid3,\n #mza-electromagnetisme-avance-cpge .method{\n   grid-template-columns:1fr\n }\n}\n<\/style>\n\n<header class=\"hero\">\n<div class=\"wrap\">\n\n<span class=\"badge\">COURS 17 \u2022 PHYSIQUE CPGE<\/span>\n\n<h1>Champs variables.<br>Maxwell. Propagation.<\/h1>\n\n<p class=\"lead\">\nL\u2019\u00e9lectromagn\u00e9tisme avanc\u00e9 unifie \u00e9lectrostatique, magn\u00e9tostatique et induction.\nLes \u00e9quations de Maxwell montrent qu\u2019un champ \u00e9lectrique variable cr\u00e9e un champ magn\u00e9tique,\net r\u00e9ciproquement, ce qui conduit naturellement aux ondes \u00e9lectromagn\u00e9tiques.\n<\/p>\n\n<div class=\"actions\">\n<a href=\"#cours\" class=\"btn gold\">\ud83d\udcda COMMENCER<\/a>\n<a href=\"#methode\" class=\"btn glass\">\ud83e\udde0 M\u00c9THODE<\/a>\n<a href=\"#exercices\" class=\"btn glass\">\ud83e\udde9 EXERCICES<\/a>\n<a href=\"#qcm\" class=\"btn glass\">\u2753 QCM<\/a>\n<\/div>\n\n<\/div>\n<\/header>\n\n<section id=\"cours\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">1. LES QUATRE \u00c9QUATIONS DE MAXWELL<\/span>\n<h2>Le socle de l\u2019\u00e9lectromagn\u00e9tisme classique.<\/h2>\n<\/div>\n\n<div class=\"grid\">\n\n<div class=\"card\">\n<h3>Maxwell-Gauss<\/h3>\n<div class=\"formula\">\n\u2207\u00b7E = \u03c1\/\u03b5\u2080\n<\/div>\n<p>Les charges \u00e9lectriques sont sources du champ \u00e9lectrique.<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Maxwell-Thomson<\/h3>\n<div class=\"formula\">\n\u2207\u00b7B = 0\n<\/div>\n<p>Il n&#8217;existe pas de monop\u00f4le magn\u00e9tique dans le cadre classique usuel.<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Maxwell-Faraday<\/h3>\n<div class=\"formula\">\n\u2207\u00d7E = -\u2202B\/\u2202t\n<\/div>\n<p>Un champ magn\u00e9tique variable cr\u00e9e un champ \u00e9lectrique tourbillonnaire.<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Maxwell-Amp\u00e8re<\/h3>\n<div class=\"formula\">\n\u2207\u00d7B = \u03bc\u2080j + \u03bc\u2080\u03b5\u2080\u2202E\/\u2202t\n<\/div>\n<p>Courants et champs \u00e9lectriques variables cr\u00e9ent du champ magn\u00e9tique.<\/p>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">2. FORMES INT\u00c9GRALES<\/span>\n<h2>Relier les champs aux surfaces et aux contours.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\n\u222f E\u00b7dS = Q<sub>int<\/sub>\/\u03b5\u2080\n<\/div>\n\n<div class=\"formula\">\n\u222f B\u00b7dS = 0\n<\/div>\n\n<div class=\"formula\">\n\u222e E\u00b7dl = -d\u03a6<sub>B<\/sub>\/dt\n<\/div>\n\n<div class=\"formula\">\n\u222e B\u00b7dl = \u03bc\u2080I<sub>traversant<\/sub> + \u03bc\u2080\u03b5\u2080 d\u03a6<sub>E<\/sub>\/dt\n<\/div>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">3. COURANT DE D\u00c9PLACEMENT<\/span>\n<h2>La correction d\u00e9cisive de Maxwell.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\nMaxwell introduit le terme :\n<\/p>\n\n<div class=\"formula\">\nj<sub>d<\/sub> = \u03b5\u2080 \u2202E\/\u2202t\n<\/div>\n\n<p>\nIl joue le r\u00f4le d&#8217;un courant associ\u00e9 \u00e0 la variation temporelle du champ \u00e9lectrique.\n<\/p>\n\n<p>\nCe terme permet notamment de conserver la coh\u00e9rence de la loi d&#8217;Amp\u00e8re dans un condensateur en charge.\n<\/p>\n\n<\/div>\n<\/section>\n\n<section id=\"methode\" class=\"dark\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\" style=\"color:#efd68c\">MZA MAXWELL ENGINE<\/span>\n<h2>Six r\u00e9flexes pour traiter un probl\u00e8me \u00e9lectromagn\u00e9tique.<\/h2>\n<\/div>\n\n<div class=\"method\">\n<div><b>01<\/b><span>SOURCES<\/span><\/div>\n<div><b>02<\/b><span>SYM\u00c9TRIES<\/span><\/div>\n<div><b>03<\/b><span>MAXWELL<\/span><\/div>\n<div><b>04<\/b><span>ONDE<\/span><\/div>\n<div><b>05<\/b><span>\u00c9NERGIE<\/span><\/div>\n<div><b>06<\/b><span>LIMITES<\/span><\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">4. CONSERVATION DE LA CHARGE<\/span>\n<h2>Une cons\u00e9quence structurelle des \u00e9quations de Maxwell.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\n\u2202\u03c1\/\u2202t + \u2207\u00b7j = 0\n<\/div>\n\n<p>\nC&#8217;est l&#8217;\u00e9quation locale de conservation de la charge \u00e9lectrique.\n<\/p>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">5. ONDES \u00c9LECTROMAGN\u00c9TIQUES DANS LE VIDE<\/span>\n<h2>Maxwell pr\u00e9dit leur existence.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\nDans le vide sans charge ni courant :\n<\/p>\n\n<div class=\"formula\">\n\u03c1 = 0\n<\/div>\n\n<div class=\"formula\">\nj = 0\n<\/div>\n\n<p>\nLes \u00e9quations de Maxwell conduisent \u00e0 :\n<\/p>\n\n<div class=\"formula\">\n\u2207\u00b2E &#8211; \u03bc\u2080\u03b5\u2080 \u2202\u00b2E\/\u2202t\u00b2 = 0\n<\/div>\n\n<div class=\"formula\">\n\u2207\u00b2B &#8211; \u03bc\u2080\u03b5\u2080 \u2202\u00b2B\/\u2202t\u00b2 = 0\n<\/div>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">6. C\u00c9L\u00c9RIT\u00c9<\/span>\n<h2>La vitesse de la lumi\u00e8re appara\u00eet naturellement.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\nc = 1\/\u221a(\u03bc\u2080\u03b5\u2080)\n<\/div>\n\n<p>\nLa c\u00e9l\u00e9rit\u00e9 des ondes \u00e9lectromagn\u00e9tiques dans le vide est donc celle de la lumi\u00e8re.\n<\/p>\n\n<div class=\"tip\">\nC&#8217;est l&#8217;une des grandes unifications de la physique : la lumi\u00e8re est une onde \u00e9lectromagn\u00e9tique.\n<\/div>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">7. ONDE PLANE PROGRESSIVE<\/span>\n<h2>Une solution fondamentale.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\nUne onde plane monochromatique se propageant selon +z peut s&#8217;\u00e9crire :\n<\/p>\n\n<div class=\"formula\">\nE(z,t)=E\u2080 cos(\u03c9t-kz+\u03c6) u<sub>x<\/sub>\n<\/div>\n\n<p>\net :\n<\/p>\n\n<div class=\"formula\">\nB(z,t)=B\u2080 cos(\u03c9t-kz+\u03c6) u<sub>y<\/sub>\n<\/div>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">8. STRUCTURE DE L&#8217;ONDE<\/span>\n<h2>E, B et direction de propagation sont orthogonaux.<\/h2>\n<\/div>\n\n<div class=\"grid3\">\n\n<div class=\"card\">\n<h3>Transversalit\u00e9<\/h3>\n<p>E est perpendiculaire \u00e0 la direction de propagation.<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Champ magn\u00e9tique<\/h3>\n<p>B est perpendiculaire \u00e0 E.<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Tri\u00e8dre direct<\/h3>\n<div class=\"formula\">\nE \u00d7 B\n<\/div>\n<p>pointe dans le sens de propagation.<\/p>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">9. RELATION ENTRE E ET B<\/span>\n<h2>Une onde \u00e9lectromagn\u00e9tique relie directement les amplitudes.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\nB\u2080 = E\u2080\/c\n<\/div>\n\n<p>\nDans le vide :\n<\/p>\n\n<div class=\"formula\">\nB = (1\/c) u \u00d7 E\n<\/div>\n\n<p>\no\u00f9 u est le vecteur unitaire dans la direction de propagation.\n<\/p>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">10. RELATION DE DISPERSION<\/span>\n<h2>Milieu non dispersif dans le vide.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\n\u03c9 = ck\n<\/div>\n\n<p>\nAinsi :\n<\/p>\n\n<div class=\"formula\">\nv<sub>\u03c6<\/sub> = \u03c9\/k = c\n<\/div>\n\n<p>\net \u00e9galement :\n<\/p>\n\n<div class=\"formula\">\nv<sub>g<\/sub> = d\u03c9\/dk = c\n<\/div>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">11. POLARISATION<\/span>\n<h2>D\u00e9crire l&#8217;\u00e9volution du champ \u00e9lectrique transversal.<\/h2>\n<\/div>\n\n<div class=\"grid3\">\n\n<div class=\"card\">\n<h3>Lin\u00e9aire<\/h3>\n<p>\nE oscille selon une direction fixe.\n<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Circulaire<\/h3>\n<p>\nL&#8217;extr\u00e9mit\u00e9 de E d\u00e9crit un cercle.\n<\/p>\n<\/div>\n\n<div class=\"card\">\n<h3>Elliptique<\/h3>\n<p>\nCas g\u00e9n\u00e9ral : l&#8217;extr\u00e9mit\u00e9 de E d\u00e9crit une ellipse.\n<\/p>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">12. \u00c9NERGIE DU CHAMP \u00c9LECTROMAGN\u00c9TIQUE<\/span>\n<h2>Les champs transportent de l&#8217;\u00e9nergie.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\nDensit\u00e9 volumique d&#8217;\u00e9nergie \u00e9lectrique :\n<\/p>\n\n<div class=\"formula\">\nu<sub>E<\/sub> = \u00bd\u03b5\u2080E\u00b2\n<\/div>\n\n<p>\nDensit\u00e9 volumique d&#8217;\u00e9nergie magn\u00e9tique :\n<\/p>\n\n<div class=\"formula\">\nu<sub>B<\/sub> = B\u00b2\/(2\u03bc\u2080)\n<\/div>\n\n<p>\nDensit\u00e9 totale :\n<\/p>\n\n<div class=\"formula\">\nu = \u00bd\u03b5\u2080E\u00b2 + B\u00b2\/(2\u03bc\u2080)\n<\/div>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">13. VECTEUR DE POYNTING<\/span>\n<h2>Le flux d&#8217;\u00e9nergie \u00e9lectromagn\u00e9tique.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\nS = (1\/\u03bc\u2080) E \u00d7 B\n<\/div>\n\n<p>\nS donne la densit\u00e9 de flux de puissance \u00e9lectromagn\u00e9tique.\nSon unit\u00e9 est W\u00b7m\u207b\u00b2.\n<\/p>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">14. INTENSIT\u00c9 MOYENNE D&#8217;UNE ONDE SINUSO\u00cfDALE<\/span>\n<h2>Passer des champs \u00e0 une puissance mesurable.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\nPour une onde plane monochromatique dans le vide :\n<\/p>\n\n<div class=\"formula\">\n&lt;S&gt; = \u00bd \u03b5\u2080 c E\u2080\u00b2\n<\/div>\n\n<p>\nOn peut aussi \u00e9crire :\n<\/p>\n\n<div class=\"formula\">\n&lt;S&gt; = E\u2080\u00b2\/(2\u03bc\u2080c)\n<\/div>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">15. CONSERVATION DE L&#8217;\u00c9NERGIE \u00c9LECTROMAGN\u00c9TIQUE<\/span>\n<h2>Th\u00e9or\u00e8me de Poynting.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<div class=\"formula\">\n\u2202u\/\u2202t + \u2207\u00b7S = -j\u00b7E\n<\/div>\n\n<p>\nCette relation exprime le bilan local d&#8217;\u00e9nergie entre champs et mati\u00e8re.\n<\/p>\n\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">16. R\u00c9FLEXION SUR UN CONDUCTEUR PARFAIT<\/span>\n<h2>Des conditions aux limites imposent une onde r\u00e9fl\u00e9chie.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\n\u00c0 la surface d&#8217;un conducteur parfait, le champ \u00e9lectrique tangent doit s&#8217;annuler.\nUne onde incidente doit donc se superposer \u00e0 une onde r\u00e9fl\u00e9chie.\n<\/p>\n\n<p>\nCela peut conduire \u00e0 la formation d&#8217;ondes stationnaires \u00e9lectromagn\u00e9tiques.\n<\/p>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">17. PRESSION DE RADIATION<\/span>\n<h2>Une onde transporte aussi de la quantit\u00e9 de mouvement.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<p>\nPour une onde absorb\u00e9e par une surface id\u00e9ale :\n<\/p>\n\n<div class=\"formula\">\np<sub>rad<\/sub> = I\/c\n<\/div>\n\n<p>\nPour une r\u00e9flexion parfaite normale :\n<\/p>\n\n<div class=\"formula\">\np<sub>rad<\/sub> = 2I\/c\n<\/div>\n\n<\/div>\n<\/section>\n\n<section id=\"exercices\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">18. EXERCICES PROGRESSIFS<\/span>\n<h2>Maxwell, onde, \u00e9nergie.<\/h2>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU 1<\/span>\n<h3>Exercice 1 \u2014 Relation E-B<\/h3>\n<p>\nUne onde \u00e9lectromagn\u00e9tique plane dans le vide poss\u00e8de une amplitude \u00e9lectrique E0.\nExprimer B0.\n<\/p>\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaEmHint('emHint1')\">\ud83d\udca1 INDICE<\/button>\n<div id=\"emHint1\" class=\"hint\">\nDans le vide, les amplitudes v\u00e9rifient B0=E0\/c.\n<\/div>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU 2<\/span>\n<h3>Exercice 2 \u2014 C\u00e9l\u00e9rit\u00e9<\/h3>\n<p>\n\u00c0 partir de l&#8217;\u00e9quation d&#8217;onde issue de Maxwell, identifier la c\u00e9l\u00e9rit\u00e9 de propagation.\n<\/p>\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaEmHint('emHint2')\">\ud83d\udca1 INDICE<\/button>\n<div id=\"emHint2\" class=\"hint\">\nComparez avec l&#8217;\u00e9quation g\u00e9n\u00e9rale \u2207\u00b2s-(1\/c\u00b2)\u2202\u00b2s\/\u2202t\u00b2=0.\n<\/div>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU 3<\/span>\n<h3>Exercice 3 \u2014 Poynting<\/h3>\n<p>\nUne onde poss\u00e8de des champs E et B orthogonaux. D\u00e9terminer la direction de propagation \u00e9nerg\u00e9tique.\n<\/p>\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaEmHint('emHint3')\">\ud83d\udca1 INDICE<\/button>\n<div id=\"emHint3\" class=\"hint\">\nUtilisez le produit vectoriel E\u00d7B.\n<\/div>\n<\/div>\n\n<div class=\"exercise\">\n<span class=\"level\">NIVEAU PR\u00c9PA<\/span>\n<h3>Exercice 4 \u2014 \u00c9nergie moyenne<\/h3>\n<p>\nUne onde plane monochromatique poss\u00e8de une amplitude \u00e9lectrique E0.\nExprimer son intensit\u00e9 moyenne dans le vide.\n<\/p>\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaEmHint('emHint4')\">\ud83d\udca1 INDICE<\/button>\n<div id=\"emHint4\" class=\"hint\">\nLa moyenne temporelle de cos\u00b2 vaut 1\/2.\n<\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<section style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">19. PROBLEM LAB<\/span>\n<h2>Mission : onde \u00e9lectromagn\u00e9tique re\u00e7ue par une antenne.<\/h2>\n<\/div>\n\n<div class=\"card\">\n\n<h3>Situation<\/h3>\n\n<p>\nUne onde plane monochromatique arrive sur une antenne.\nLe champ \u00e9lectrique incident est connu sous la forme :\n<\/p>\n\n<div class=\"formula\">\nE(z,t)=E\u2080 cos(\u03c9t-kz) u<sub>x<\/sub>\n<\/div>\n\n<p>Votre mission :<\/p>\n\n<ol>\n<li>identifier la direction de propagation ;<\/li>\n<li>d\u00e9terminer la direction du champ magn\u00e9tique ;<\/li>\n<li>exprimer B(z,t) ;<\/li>\n<li>relier k et \u03c9 ;<\/li>\n<li>calculer la densit\u00e9 d&#8217;\u00e9nergie \u00e9lectromagn\u00e9tique instantan\u00e9e ;<\/li>\n<li>calculer le vecteur de Poynting ;<\/li>\n<li>d\u00e9terminer l&#8217;intensit\u00e9 moyenne ;<\/li>\n<li>\u00e9tudier l&#8217;effet d&#8217;un doublement de E0 ;<\/li>\n<li>discuter le r\u00f4le de la polarisation sur la r\u00e9ception par l&#8217;antenne ;<\/li>\n<li>expliquer ce qui change si l&#8217;onde rencontre un conducteur parfait.<\/li>\n<\/ol>\n\n<div class=\"actions\">\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaEmHint('emMission1')\">\ud83d\udca1 INDICE<\/button>\n<button type=\"button\" class=\"btn\" style=\"background:#06172c;color:#fff\" onclick=\"mzaEmHint('emMission2')\">\ud83e\udde0 M\u00c9THODE<\/button>\n<\/div>\n\n<div id=\"emMission1\" class=\"hint\">\nCommencez par le tri\u00e8dre E, B, propagation. Ensuite seulement calculez \u00e9nergie et Poynting.\n<\/div>\n\n<div id=\"emMission2\" class=\"hint\">\nProc\u00e9dez dans l&#8217;ordre : phase \u2192 direction \u2192 B \u2192 relation de dispersion \u2192 \u00e9nergie \u2192 Poynting \u2192 moyenne temporelle \u2192 interpr\u00e9tation physique.\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section class=\"dark\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\" style=\"color:#efd68c\">MZA MAXWELL CHECK<\/span>\n<h2>Les six r\u00e9flexes d&#8217;\u00e9lectromagn\u00e9tisme avanc\u00e9.<\/h2>\n<\/div>\n\n<div class=\"method\">\n<div><b>A<\/b><span>MAXWELL<\/span><\/div>\n<div><b>B<\/b><span>TRANSVERSALIT\u00c9<\/span><\/div>\n<div><b>C<\/b><span>\u03c9 \/ k<\/span><\/div>\n<div><b>D<\/b><span>E \/ B<\/span><\/div>\n<div><b>E<\/b><span>POYNTING<\/span><\/div>\n<div><b>F<\/b><span>\u00c9NERGIE<\/span><\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<section id=\"qcm\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">20. QCM DE VALIDATION<\/span>\n<h2>Diagnostic \u00c9lectromagn\u00e9tisme avanc\u00e9 CPGE.<\/h2>\n<p>Le score est affich\u00e9 sans r\u00e9v\u00e9ler les r\u00e9ponses correctes.<\/p>\n<\/div>\n\n<div class=\"qcm\">\n\n<form id=\"emQuiz\">\n\n<div class=\"question\">\n<strong>1. Dans le vide, l&#8217;\u00e9quation de Maxwell-Gauss sans charge donne :<\/strong>\n<label><input type=\"radio\" name=\"em1\" value=\"1\"> \u2207\u00b7E=0<\/label>\n<label><input type=\"radio\" name=\"em1\" value=\"0\"> \u2207\u00d7E=0 toujours<\/label>\n<label><input type=\"radio\" name=\"em1\" value=\"0\"> E=0 n\u00e9cessairement<\/label>\n<label><input type=\"radio\" name=\"em1\" value=\"0\"> \u2207\u00b7B=\u03c1\/\u03b5\u2080<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>2. La c\u00e9l\u00e9rit\u00e9 d&#8217;une onde \u00e9lectromagn\u00e9tique dans le vide vaut :<\/strong>\n<label><input type=\"radio\" name=\"em2\" value=\"1\"> 1\/\u221a(\u03bc\u2080\u03b5\u2080)<\/label>\n<label><input type=\"radio\" name=\"em2\" value=\"0\"> \u221a(\u03bc\u2080\u03b5\u2080)<\/label>\n<label><input type=\"radio\" name=\"em2\" value=\"0\"> \u03bc\u2080\/\u03b5\u2080<\/label>\n<label><input type=\"radio\" name=\"em2\" value=\"0\"> \u03b5\u2080\/\u03bc\u2080<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>3. Dans une onde plane dans le vide :<\/strong>\n<label><input type=\"radio\" name=\"em3\" value=\"1\"> E, B et la direction de propagation sont orthogonaux<\/label>\n<label><input type=\"radio\" name=\"em3\" value=\"0\"> E est parall\u00e8le \u00e0 B<\/label>\n<label><input type=\"radio\" name=\"em3\" value=\"0\"> E est toujours nul<\/label>\n<label><input type=\"radio\" name=\"em3\" value=\"0\"> B est longitudinal<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>4. La relation entre les amplitudes vaut :<\/strong>\n<label><input type=\"radio\" name=\"em4\" value=\"1\"> B0=E0\/c<\/label>\n<label><input type=\"radio\" name=\"em4\" value=\"0\"> B0=cE0<\/label>\n<label><input type=\"radio\" name=\"em4\" value=\"0\"> E0=B0<\/label>\n<label><input type=\"radio\" name=\"em4\" value=\"0\"> B0=E0\u00b2<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>5. Le vecteur de Poynting s&#8217;\u00e9crit :<\/strong>\n<label><input type=\"radio\" name=\"em5\" value=\"1\"> S=(1\/\u03bc\u2080)E\u00d7B<\/label>\n<label><input type=\"radio\" name=\"em5\" value=\"0\"> S=E+B<\/label>\n<label><input type=\"radio\" name=\"em5\" value=\"0\"> S=EB scalaire uniquement<\/label>\n<label><input type=\"radio\" name=\"em5\" value=\"0\"> S=\u03bc\u2080E\u00d7B<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>6. Une onde \u00e9lectromagn\u00e9tique dans le vide v\u00e9rifie :<\/strong>\n<label><input type=\"radio\" name=\"em6\" value=\"1\"> \u03c9=ck<\/label>\n<label><input type=\"radio\" name=\"em6\" value=\"0\"> \u03c9=k\/c<\/label>\n<label><input type=\"radio\" name=\"em6\" value=\"0\"> \u03c9=c\/k<\/label>\n<label><input type=\"radio\" name=\"em6\" value=\"0\"> \u03c9 et k sont ind\u00e9pendants<\/label>\n<\/div>\n\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaEmScore()\">\nVALIDER MON QCM\n<\/button>\n\n<\/form>\n\n<div id=\"emResult\"><\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<section>\n<div class=\"wrap\">\n\n<div class=\"cta\">\n\n<div style=\"font-size:43px\">c = 1 \/ \u221a(\u03bc\u2080\u03b5\u2080)<\/div>\n\n<h2>Maxwell transforme les champs variables en lumi\u00e8re.<\/h2>\n\n<p>\nLes \u00e9quations de Maxwell, la propagation, la polarisation, le vecteur de Poynting\net la conservation de l&#8217;\u00e9nergie constituent le pont entre \u00e9lectromagn\u00e9tisme,\noptique et t\u00e9l\u00e9communications.\n<\/p>\n\n<div class=\"actions\" style=\"justify-content:center\">\n<a href=\"#cours\" class=\"btn gold\">\ud83d\udcda REVOIR LE COURS<\/a>\n<a href=\"#exercices\" class=\"btn glass\">\ud83e\udde9 EXERCICES<\/a>\n<a href=\"#qcm\" class=\"btn glass\">\u2753 REFAIRE LE QCM<\/a>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<script>\nfunction mzaEmHint(id){\n const el=document.getElementById(id);\n if(!el)return;\n el.style.display = el.style.display===\"block\" ? \"none\" : \"block\";\n}\n\nfunction mzaEmScore(){\n const form=document.getElementById(\"emQuiz\");\n const result=document.getElementById(\"emResult\");\n\n let score=0;\n let complete=true;\n\n [\"em1\",\"em2\",\"em3\",\"em4\",\"em5\",\"em6\"].forEach(function(name){\n   const answer=form.querySelector('input[name=\"'+name+'\"]:checked');\n\n   if(!answer){\n     complete=false;\n   }else{\n     score+=Number(answer.value);\n   }\n });\n\n result.style.display=\"block\";\n\n if(!complete){\n   result.innerHTML=\"<strong>R\u00e9pondez aux 6 questions avant de valider.<\/strong>\";\n   return;\n }\n\n const pct=Math.round(score\/6*100);\n\n let level=\"\u00c9lectromagn\u00e9tisme avanc\u00e9 \u00e0 consolider\";\n if(pct>=50) level=\"Fondations acquises\";\n if(pct>=67) level=\"Bon niveau\";\n if(pct>=84) level=\"Tr\u00e8s bonne ma\u00eetrise\";\n if(pct===100) level=\"Excellent niveau CPGE\";\n\n result.innerHTML=\n \"<strong style='font-size:30px;color:#efd68c'>\"+pct+\"%<\/strong>\"+\n \"<p><b>\"+level+\"<\/b><\/p>\"+\n \"<p>Score : \"+score+\" \/ 6<\/p>\"+\n \"<p>Les r\u00e9ponses correctes et la correction d\u00e9taill\u00e9e restent masqu\u00e9es.<\/p>\";\n}\n<\/script>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>&#8220;`html COURS 17 \u2022 PHYSIQUE CPGE Champs variables.Maxwell. Propagation. L\u2019\u00e9lectromagn\u00e9tisme avanc\u00e9 unifie \u00e9lectrostatique, magn\u00e9tostatique et induction. Les \u00e9quations de Maxwell montrent qu\u2019un champ \u00e9lectrique variable cr\u00e9e un champ magn\u00e9tique, et r\u00e9ciproquement, ce qui conduit naturellement aux ondes \u00e9lectromagn\u00e9tiques. \ud83d\udcda COMMENCER \ud83e\udde0 M\u00c9THODE \ud83e\udde9 EXERCICES \u2753 QCM 1. LES QUATRE \u00c9QUATIONS DE MAXWELL Le socle de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1620","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1620","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/comments?post=1620"}],"version-history":[{"count":1,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1620\/revisions"}],"predecessor-version":[{"id":1623,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1620\/revisions\/1623"}],"wp:attachment":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/media?parent=1620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}