Update cheatsheet.en.md

12.temporary_ins/90.electromagnetism-in-vacuum/10.maxwell-equations/20.overview/cheatsheet.en.md

@@ -263,7 +263,7 @@ _thus revolutionizing physics._
    \end{array}`$**
    <br>
    * This equation plays an *important role in Neumann's induction phenomena*.
-   The quantity $`\oint_{\Gamma\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}`
+   The quantity $`\oint_{\Gamma\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl}`$ 
    with the historically imperfect name "electromotive force (emf)", homogeneous to a voltage, is the origin of an electric current
    flowing through the contour $`\Gamma`$ if it represents a conductive circuit.
 
@@ -336,7 +336,7 @@ _thus revolutionizing physics._
   ! *leaving it is equal to the change in charge within the volume.*
 
   <br>
-  This is expressed mathematically by the **integral expression**:
+  This is expressed mathematically by the **integral expression** :   
   <br>
   For any closed surface $`S`$ bounding a macroscopic volume $`\tau`$,   
   <br>
@@ -350,7 +350,7 @@ _thus revolutionizing physics._
   ![Charge conservation law](charge-conservation-law-L1200.jpg)
 
 * Since this equality holds for any integration volume, it must apply to the integrands themselves.
-  $`\Longrightarrow`$ The conservation law also has a **local expression**, valid at every point in space, which is written as:
+  $`\Longrightarrow`$ The conservation law also has a **local expression**, valid at every point in space, which is written as :   
   <br>
   **$`\mathbf{\text{div}\,\overrightarrow{j} +\dfrac{\partial \dens}{\partial t}=0}`$**   
 
@@ -373,7 +373,7 @@ _thus revolutionizing physics._
   **$`\mathbf{\text{div}\big(\overrightarrow{\text{curl}}\,\overrightarrow{B}\big)=0}`$**.
 
 * The *Maxwell-Ampère law*   
-  $`\overrightarrow{\text{curl}}\,\overrightarrow{B}=\mu_0\,\overrightarrow{j} + \mu_0\epsilon_0 \;\dfrac{\partial \overrightarrow{E}}{\partial t}`$
+  *$`\overrightarrow{\text{curl}}\,\overrightarrow{B}=\mu_0\,\overrightarrow{j} + \mu_0\epsilon_0 \;\dfrac{\partial \overrightarrow{E}}{\partial t}`$*   
   allows us to write :   
   <br>
   **$`\mathbf{\text{div}\Big(\mu_0\,\overrightarrow{j} + \mu_0\epsilon_0 \;\dfrac{\partial \overrightarrow{E}}{\partial t}\Big)=0}`$**   
@@ -558,7 +558,7 @@ I recognize here the law of conservation of charge.
 ! The *magnetic force $`\overrightarrow{F}_{magn.}=q\,\overrightarrow{v}\times\overrightarrow{B}`$*,
 ! by nature perpendicular to the velocity vector $`\overrightarrow{v}`$ and thus to the elementary displacement
 ! vector $`\overrightarrow{dl}=\overrightarrow{v}\,dt`$ at every point on the particle's trajectory
-! with charge $`q`$*, *does no work*:
+! with charge $`q`$*, *does no work* :   
 !
 ! $`\mathbf{d\mathcal{W}_{magn} = \overrightarrow{F}_{magn}\cdot \overrightarrow{dl}=0}`$
 !
@@ -723,7 +723,7 @@ I recognize here the law of conservation of charge.
 
 * To **establish the expression $`\Delta \overrightarrow{E}`$**, I calculate
   $`\overrightarrow{\text{curl}}\left(\overrightarrow{\text{curl}} \overrightarrow{E}\right)`$ and then
-  $`\overrightarrow{\text{grad}} \left(\text{div} \overrightarrow{E}\right)`$* from Maxwell's equations.
+  $`\overrightarrow{\text{grad}} \left(\text{div} \overrightarrow{E}\right)`$ *from Maxwell's equations*.
 
 * $`\overrightarrow{\text{curl}} \left(\overrightarrow{\text{curl}} \overrightarrow{E}\right) =
   \overrightarrow{\text{curl}} \left(-\dfrac{\partial \overrightarrow{B}}{\partial t}\right)`$   
@@ -860,6 +860,31 @@ I recognize here the law of conservation of charge.
 !! *Relativistic physics in the general sense*:
 !! spacetime-matter-energy.
 
+#### What Is the Electromagnetic Spectrum?
+
+* **Maxwell** hypothesized that *visible light*, whose speed had just been measured from
+  astronomical observations of the motion of Jupiter's satellites, *is an electromagnetic wave*.   
+  <br>
+  $`\Longrightarrow`$ Light is only a tiny part of electromagnetic waves.   
+  <br>
+  $`\Longrightarrow`$ A *whole new world of "lights"* is revealed, called the **electromagnetic spectrum**.   
+
+![Electromagnetic Spectrum](astro-electromagnetic-spectrum-N4_1_fr_L1200.jpg)
+
+* In particular, **knowledge of the universe** resulted *before Maxwell* from the sole observation of the *visible domain*,   
+
+![Visible Sky](ciel-visible-bsp_L1200.jpg)
+
+* now extends to *the entire electromagnetic spectrum*.
+
+![Sky in Various Wavelengths](ciel-images-bsp_L600_transparence.gif)
+
+<br>
+
+------
+
+<br>
+
 <br>
 
 -------
@@ -1000,30 +1025,7 @@ Some very concise ideas.
 For transverse and classical resources, parallel links
 ---------------------->
 
-#### What Is the Electromagnetic Spectrum?
-
-* **Maxwell** hypothesized that *visible light*, whose speed had just been measured from
-  astronomical observations of the motion of Jupiter's satellites, *is an electromagnetic wave*.   
-  <br>
-  $`\Longrightarrow`$ Light is only a tiny part of electromagnetic waves.   
-  <br>
-  $`\Longrightarrow`$ A *whole new world of "lights"* is revealed, called the **electromagnetic spectrum**.   
-
-![Electromagnetic Spectrum](astro-electromagnetic-spectrum-N4_1_en_L1200.jpg)
-
-* In particular, **knowledge of the universe** resulted *before Maxwell* from the sole observation of the *visible domain*,   
 
-![Visible Sky](ciel-visible-bsp_L1200.jpg)
-
-* now extends to *the entire electromagnetic spectrum*.
-
-![Sky in Various Wavelengths](ciel-images-bsp_L600_transparence.gif)
-
-<br>
-
-------
-
-<br>