Update cheatsheet.fr.md

12.temporary_ins/90.electromagnetism-in-vacuum/20.electromagnetic-waves-vacuum/20.overview/cheatsheet.fr.md

@@ -176,9 +176,9 @@ puis d'une onde plane progressive monochromatique (OPPM).
     &\dfrac{\partial E_x}{\partial z}-\dfrac{\partial E_z}{\partial x}=-\dfrac{\partial B_y}{\partial t}\\
     &\dfrac{\partial E_y}{\partial x}-\dfrac{\partial E_x}{\partial y}=-\dfrac{\partial B_z}{\partial t}\\
     \\
-    &\dfrac{\partial E_z}{\partial y}=\dfrac{\partial E_y}{\partial z}=\dfrac{\partial E_x}{\partial z}\\
-    &\quad =\dfrac{\partial E_z}{\partial x}=\dfrac{\partial E_y}{\partial x}=\dfrac{\partial E_x}{\partial y}=0
-    \end{align}\right.`$   
+    &\dfrac{\partial E_z}{\partial y}=\dfrac{\partial E_y}{\partial z}=\dfrac{\partial E_x}{\partial z}=\dfrac{\partial E_z}{\partial x}\\
+    &\quad =\dfrac{\partial E_y}{\partial x}=\dfrac{\partial E_x}{\partial y}=0
+    \end{align}\right\}`$   
     <br>
     *$`\Longrightarrow\left\{
     \begin{align}
@@ -215,7 +215,7 @@ puis d'une onde plane progressive monochromatique (OPPM).
   $`\left.
     \begin{align} 
     &\underbrace{\overrightarrow{rot}\,\overrightarrow{B}=
-    \mu_0\,\overrightarrow{j}+\mu_0\epsilon_0\,\dfrac{\partial \overrightarrow{E}}{\partial t}}_{\color{blue}{\text{th. de Maxwell-Faraday}}}
+    \mu_0\,\overrightarrow{j}+\upperbrace{\mu_0\epsilon_0}^{=\;\dfrac{1}{c^2}}\,\dfrac{\partial \overrightarrow{E}}{\partial t}}_{\color{blue}{\text{th. de Maxwell-Faraday}}}
      =\dfrac{1}{c^2}\,\dfrac{\partial \overrightarrow{E}}{\partial t}\\
     \\
     &\overrightarrow{B}\;uniforme\\
@@ -223,19 +223,19 @@ puis d'une onde plane progressive monochromatique (OPPM).
     <br>
     $`\Longrightarrow\left\{
     \begin{align}
-    &\dfrac{\partial B_z}{\partial y}-\dfrac{\partial B_y}{\partial z}=\dfrac{\partial E_x}{\partial t}\\
-    &\dfrac{\partial E_x}{\partial z}-\dfrac{\partial E_z}{\partial x}=-\dfrac{\partial B_y}{\partial t}\\
-    &\dfrac{\partial E_y}{\partial x}-\dfrac{\partial E_x}{\partial y}=-\dfrac{\partial B_z}{\partial t}\\
+    &\dfrac{\partial B_z}{\partial y}-\dfrac{\partial B_y}{\partial z}=\dfrac{1}{c^2}\;\dfrac{\partial E_x}{\partial t}\\
+    &\dfrac{\partial B_x}{\partial z}-\dfrac{\partial B_z}{\partial x}=\dfrac{1}{c^2}\;\dfrac{\partial E_y}{\partial t}}\\
+    &\dfrac{\partial B_y}{\partial x}-\dfrac{\partial B_x}{\partial y}==\dfrac{1}{c^2}\;\dfrac{\partial E_z}{\partial t}\\
     \\
-    &\dfrac{\partial E_z}{\partial y}=\dfrac{\partial E_y}{\partial z}=\dfrac{\partial E_x}{\partial z}\\
-    &\quad =\dfrac{\partial E_z}{\partial x}=\dfrac{\partial E_y}{\partial x}=\dfrac{\partial E_x}{\partial y}=0
-    \end{align}\right.`$   
+    &\dfrac{\partial B_z}{\partial y}=\dfrac{\partial B_y}{\partial z}=\dfrac{\partial B_x}{\partial z}=\dfrac{\partial B_z}{\partial x}\\
+    &\quad =\dfrac{\partial B_y}{\partial x}=\dfrac{\partial B_x}{\partial y}=0
+    \end{align}\right\}`$   
     <br>
     *$`\Longrightarrow\left\{
     \begin{align}
-    &\dfrac{\partial B_x}{\partial t}=- \dfrac{\partial E_y}{\partial z}\\
+    &-\dfrac{\partial B_z}{\partial x}=\dfrac{1}{c^2}\;\dfrac{\partial E_y}{\partial t}\\
     \\
-    &\dfrac{\partial B_y}{\partial t}=- \dfrac{\partial E_x}{\partial z}\\
+    &\dfrac{\partial B_y}{\partial x}=\dfrac{1}{c^2}\;\dfrac{\partial E_z}{\partial t}\\
     \\
     &\dfrac{\partial B_z}{\partial t}=0
     \end{align}\right.`$*