From fd4e52f613509aa93b6053b3725ae1db226b7d79 Mon Sep 17 00:00:00 2001
From: Claude Meny <claude.meny@irap.omp.eu>
Date: Tue, 19 Nov 2019 20:47:44 +0100
Subject: [PATCH] Update textbook.en.md

---
 .../textbook.en.md                            | 39 +++++++++++++++----
 1 file changed, 31 insertions(+), 8 deletions(-)

diff --git a/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md b/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
index dbcde9782..46ccffda0 100644
--- a/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
+++ b/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
@@ -746,19 +746,39 @@ $`=\dfrac{1}{\epsilon_0} \cdot \displaystyle\iiint_{\tau\leftrightarrow S} \rho
 
 $`\displaystyle\oiint_S\overrightarrow{B}\cdot\overrightarrow{dS}=0`$
 -->
+------------------------
 
-
-* **Ley de Gauss = teorema de Gauss** / Théorème de Gauss / Gauss' theorem
+* **Ley de Gauss = teorema de Gauss / Théorème de Gauss / Gauss' theorem**
 
 $`\displaystyle\iiint_{\tau} div\overrightarrow{E} \cdot d\tau= \displaystyle\iiint_{\tau}
 \dfrac{\rho}{\epsilon_0} \cdot d\tau = \dfrac{1}{\epsilon_0} \cdot \iiint_{\tau} \rho 
 \cdot d\tau = \dfrac{Q_{int}}{\epsilon_0} `$
 
+
+Ostrogradsky’s theorem = divergence theorem : for all vectorial field $`\vec{X}`$, $`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau = \displaystyle 
+\oiint_{S\leftrightarrow\tau} \overrightarrow{X}\cdot\overrightarrow{dS}`$
+
+$`\displaystyle\iiint_{\tau} div\;\overrightarrow{E} \cdot d\tau = \displaystyle 
+\oiint_{S\leftrightarrow\tau} \overrightarrow{E}\cdot\overrightarrow{dS}` = \Phi_E`$
+
+$`\Phi_E`$ : Flujo eléctrico /
+
+$`\Phi_E = \displaystyle \oiint_{S\leftrightarrow\tau} \overrightarrow{E}\cdot\overrightarrow{dS}
+= \dfrac{1}{\epsilon_0} \cdot \iiint_{\tau} \rho \cdot d\tau = \dfrac{Q_{int}}{\epsilon_0} `$
+
+--------------------
+
+* **Ley de Faraday / Loi de Faraday**
+
+
 $`\displaystyle\iint_S \overrightarrow{rot} \,\overrightarrow{E}\cdot \overrightarrow{dS}
 = -\displaystyle\iint_{S \leftrightarrow \tau} \dfrac{\partial \overrightarrow{B}}{\partial t}\cdot \overrightarrow{dS}`$
 
-Mecánica newtoniana : espacio y el tiempo son desacoplados $`\Longrightarrow`$ orden de integración / derivación entre variables de espacio y tiempo no importa.
-
+Mecánica newtoniana : espacio y el tiempo son desacoplados $`\Longrightarrow`$ orden de integración
+/ derivación entre variables de espacio y tiempo no importa.<br>
+Mécanique newtonienne : espace et temps sont découplés $`\Longrightarrow`$ l'ordre d'intégration / différenciation entre 
+variables d'espace et de temps n'importe pas.
+ 
 $`\displaystyle\iint_S \overrightarrow{rot}\,\overrightarrow{E}\cdot \overrightarrow{dS} 
 = - \dfrac{\partial}{\partial t} \left( \displaystyle\iint_S \overrightarrow{B}\cdot \overrightarrow{dS}\right)`$
 
@@ -767,16 +787,19 @@ Stokes' theorem  : for all vectorial field $`\vec{X}`$, $`\displaystyle\iint_{S\
 
 $`\displaystyle\iint_{S\,orient.} \overrightarrow{rot} \,\overrightarrow{E}\cdot \overrightarrow{dS}
 = \displaystyle \oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}
-= -\displaystyle\iint_{S \leftrightarrow \tau} \dfrac{\partial \overrightarrow{B}}{\partial t}\cdot \overrightarrow{dS}`$
+= fem = \mathcal{C}_E`$
+
+$`\mathcal{C}_E` = fem = \mathcal{E}`$ : circulación del campo eléctrico = *fuerza electromotriz = voltaje inducido*
+
+$`fem = \mathcal{C}_E = \displaystyle \oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}`$ 
+
 
 
 
 
-Ostrogradsky’s theorem = divergence theorem (= Gauss's theorem) :
 
-for all vectorial field $`\vec{X}`$, 
 
-$`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau = \displaystyle 
+Ostrogradsky’s theorem = divergence theorem : for all vectorial field $`\vec{X}`$, $`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau = \displaystyle 
 \oiint_{S\leftrightarrow\tau} \overrightarrow{X}\cdot\overrightarrow{dS}`$
 
 Stokes' theorem =