From 55bf8a8387893547c0172594e68d66818a01ba9e Mon Sep 17 00:00:00 2001
From: Orestis <orestis.malaspinas@pm.me>
Date: Sun, 7 Mar 2021 20:58:24 +0100
Subject: [PATCH] updates

---
 03_charge_electrique_champs_electrique.md |  30 +-
 figs/flux_a.svg                           | 616 +++++++++++++++
 figs/flux_cube.svg                        | 857 ++++++++++++++++++++
 figs/metal_box.svg                        | 661 ++++++++++++++++
 figs/metal_box_sol.svg                    | 912 ++++++++++++++++++++++
 5 files changed, 3071 insertions(+), 5 deletions(-)
 create mode 100644 figs/flux_a.svg
 create mode 100644 figs/flux_cube.svg
 create mode 100644 figs/metal_box.svg
 create mode 100644 figs/metal_box_sol.svg

diff --git a/03_charge_electrique_champs_electrique.md b/03_charge_electrique_champs_electrique.md
index 136a9b3..a1475dd 100644
--- a/03_charge_electrique_champs_electrique.md
+++ b/03_charge_electrique_champs_electrique.md
@@ -668,7 +668,7 @@ devienne nul (et qu'ainsi ils ne bougent plus).
 
 Cette propriété a un certain nombre de conséquences intéressantes.
 
-![Le champs électrique à l'intérieur d'un conducteur est nul. Les charges se déplacent pour se placer àa la surface du conducteur et annulent exactement le champs électrique externe.](figs/field_conductor.svg){#fig:field_conductor width=80%}
+![Le champs électrique à l'intérieur d'un conducteur est nul. Les charges se déplacent pour se placer à la surface du conducteur et annulent exactement le champs électrique externe.](figs/field_conductor.svg){#fig:field_conductor width=80%}
 
 1. Toute charge nette dans un conducteur se distribue à sa surface. Pour des charges
 négatives, on peut assez aisément imaginer que les électrons essaient de s'éloigner les plus
@@ -688,6 +688,8 @@ Question (Cage de Faraday) #
 Une boîte en métal est placée entre deux plaques parallèles chargées électriquement
 comme sur @fig:metal_box.
 
+![Deux plaques charges parallèles et une boîte entre les deux.](figs/metal_box.svg){#fig:metal_box width=80%}
+
 Quel sera le champs électrique à l'intérieur de la boîte?
 
 ---
@@ -705,9 +707,11 @@ le champs électrique soit nul à l'intérieur.
 Le champs externe ne sera pas modifié, car les électrons externes se redistribueront
 exactement de la même manière que pour la boîte pleine. Cela entraîne que le champs à l'intérieur
 sera également nul, car la distribution externe des électrons sera la même que dans le cas de la boîte
-pleine. On voit qu'une cage métallique est bon moyen d'isoler un volume d'un champs électromagnétique externe à la boîte. Ainsi, une voiture frappée par la foudre protégera ses occupants tout comme un avion ne sera en général que légèrement impacté s'il reçoit la foudre.
+pleine. On voit qu'une cage métallique est bon moyen d'isoler un volume d'un champs électromagnétique externe à la boîte (voir @fig:metal_box_sol). Ainsi, une voiture frappée par la foudre protégera ses occupants tout comme un avion ne sera en général que légèrement impacté s'il reçoit la foudre.
 Contrairement à être sous un arbre pendant un orage...
 
+![Le champs électrique à l'intérieur de la boîte est nul. En effet les charges se répartissent à la surface du conducteur pour y annuler le champs.](figs/metal_box_sol.svg){#fig:metal_box_sol width=80%}
+
 ---
 
 ## La loi de Gauss
@@ -716,13 +720,29 @@ La loi de Gauss (célèbre mathématicien et physicien de 18-19e siècle) fait i
 le concept de **flux électrique**. Cette quantité est la quantité de champs électrique
 passant au travers d'une **surface**. L'équivalent pour un liquide serait le **débit** 
 (la quantité de liquide passant au travers d'une surface).
-Pour un champs électrique *uniforme*, $\vec E$, passant au travers d'une surface $S$,
+Pour un champs électrique *uniforme*, $\vec E$, passant au travers d'une surface $S$ (voir @fig:flux_a),
 comme sur @fig:flux_a le flux, $\Phi_E$ est donné par
 $$
-\Phi_E=E\cdot A\cdot \cos(\theta).
+\Phi_E=E\cdot S\cdot \cos(\theta),
 $$
+ou $\theta$ est l'angle entre la normale de la surface et la direction du champs électrique.
+
+![Le champs $\vec E$ passant au travers de la surface $S$.](figs/flux_a.svg){#fig:flux_a width=80%}
+
+Le flux électrique peut être vu de façon équivalent comme la projection de la surface sur
+la direction du champs électrique ou la projection du champs électrique sur
+le vecteur normal de la surface.
+$$
+\Phi_E=E_\perp\cdot S=E\cdot S_\perp=E\cdot S\cos \theta,
+$$
+où $S_\perp=S\cdot \theta$ est la projection de $\vec S$ sur la direction du champs électrique (la surface $S$ multipliée par le vecteur unitaire perpendiculaire à la surface) et $E_\perp$ la projection de $\vec E$ sur la direction normale à la surface $S$.
+
+Le théorème de Gauss implique le flux total de champs électrique sur une surface **fermée**.
+Prenons un cas simplifié pour commencer, où la surface fermée est un *cube*. On souhaite calculé
+le flux total passant dans la surface du cube (voir @fig:flux_cube). 
 
+![Le champs $\vec E$ passant au travers de la surface d'un cube. Chaque surface des facettes du cube est numérotée $\Delta S_1$, $\Delta S_2$, $\Delta S_3$, ..., $\Delta S_6$.](figs/flux_cube.svg){#fig:flux_a width=80%}
 
-<!-- TODO: ajouter une figure -->
+Pour ce faire nous numérotons les facettes du cube $\Delta S_1$, $\Delta S_2$, ..., $\Delta S_6$ (voir @fig:delta_cube)
 
 
diff --git a/figs/flux_a.svg b/figs/flux_a.svg
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-- 
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