Update cheatsheet.en.md

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

@@ -363,22 +363,22 @@ _thus revolutionizing physics._
 ##### Study of Maxwell's equations
 
 * **Let's start** with the remarkable operator combination, valid for any vector field $`\overrightarrow{U}`$,
-  which states:
+  which states :   
   *"The divergence of the curl of a vector field is always zero."*   
   <br>
   $`\forall \overrightarrow{X}\big(\overrightarrow{r},t\big)\;,`$*\$`\quad \mathbf{\text{div}\big(\overrightarrow{\text{curl}}\,\overrightarrow{X}\big)=0}`$*.
   <br>
-  and apply it to the magnetic induction field $`\overrightarrow{B}`$:
+  and apply it to the magnetic induction field $`\overrightarrow{B}`$ :   
   <br>
   **$`\mathbf{\text{div}\big(\overrightarrow{\text{curl}}\,\overrightarrow{B}\big)=0}`$**.
 
 * The *Maxwell-Ampère law*
-  *$`\overrightarrow{\text{curl}}\,\overrightarrow{B}=\mu_0\,\overrightarrow{j} + \mu_0\epsilon_0 \;\dfrac{\partial \overrightarrow{E}}{\partial t}`\$*
-  allows us to write:
+  $`\overrightarrow{\text{curl}}\,\overrightarrow{B}=\mu_0\,\overrightarrow{j} + \mu_0\epsilon_0 \;\dfrac{\partial \overrightarrow{E}}{\partial t}`$
+  allows us to write :   
   <br>
   **$`\mathbf{\text{div}\Big(\mu_0\,\overrightarrow{j} + \mu_0\epsilon_0 \;\dfrac{\partial \overrightarrow{E}}{\partial t}\Big)=0}`$**
 
-* Dividing both sides by $`\mu_0`$, the equation simplifies to:
+* Dividing both sides by $`\mu_0`$, the equation simplifies to :   
   <br>
   $`\text{div}\Big(\overrightarrow{j} + \epsilon_0 \;\dfrac{\partial \overrightarrow{E}}{\partial t}\Big)=0`$
 
@@ -403,7 +403,7 @@ I recognize here the law of conservation of charge.
 ----------------------->
 
 * In the context of *classical physics, space and time are independent*,
-  the order of derivation with respect to a spatial variable and a time variable does not matter:
+  the order of derivation with respect to a spatial variable and a time variable does not matter :   
   <br>
   *$`\dfrac{\partial}{\partial t}\left(\dfrac{\partial}{\partial x}\right) =\dfrac{\partial}{\partial x}\left(\dfrac{\partial}{\partial t}\right)`$*
       * The divergence operator consists only of partial derivatives with respect to spatial variables.
@@ -411,13 +411,13 @@ I recognize here the law of conservation of charge.
 
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*$`\Longrightarrow\quad \text{div}\left(\dfrac{\partial}{\partial t}\right)= \dfrac{\partial}{\partial t}\left(\text{div}\right)`$*.
 
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;We obtain:
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;We obtain :   
 
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;**$`\mathbf{\text{div}\,\overrightarrow{j} + \epsilon_0 \;\dfrac{\partial}{\partial t}\left(\text{div}\,\overrightarrow{E}\right)=0}`$**
 
 * Using the *Maxwell-Gauss law $`\text{div}\,\overrightarrow{E}=\dfrac{\dens}{\epsilon_0}`$*
   <br>
-  we obtain the **local equation of conservation of electric charge** in a time-varying regime (thus always valid):
+  we obtain the **local equation of conservation of electric charge** in a time-varying regime (thus always valid) :   
   <br>
   **$`\mathbf{\text{div}\,\overrightarrow{j} +\dfrac{\partial \dens}{\partial t}=0}`$**