Update textbook.fr.md

12.temporary_ins/96.electromagnetism-in-media/20.reflexion-refraction-at-interfaces/20.metallic-waveguides/10.main/textbook.fr.md

@@ -25,30 +25,30 @@ _TE and TM waves and their corresponding standing wave behaviour along the y axi
 * For TE modes (TE = transverse-electric) we have :   
    
 $`\overrightarrow{E}_{\perp}=\underbrace{-2\,E_0\,\sin(k\cdot y\cdot \cos\,\theta)}_{\large{amplitude}}
-\times \sin\big(\underbrace{k\,\sin\,\theta}_{\large{wavevector}}\;z-\omega t\big)\overrightarrow{e_z}`$    
+\times \sin\big(\underbrace{k\,\sin\,\theta}_{\large{wavevector}}\,z-\omega t\big)\overrightarrow{e_z}`$    
    
-and    
+<br>
    
-$`\overrightarrow{B}_{\perp}=
-\left(\begin{array}{l}
+$`\overrightarrow{B}_{\perp}=`$
+$`\left(\begin{array}{l}
 0\\
--\dfrac{2\,E_0}{c}\sin\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\cdot z \cdot \sin\,\theta-\omega t)\\
--\dfrac{2\,E_0}{c}\cos\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\cdot z \cdot \sin\,\theta-\omega t)
+-\dfrac{2\,E_0}{c}\sin\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\,\sinc\,\theta\;z -\omega t)\\
+-\dfrac{2\,E_0}{c}\cos\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\,\sinc\,\theta\;z -\omega t)
 \end{array}\right)`$
 
 * Similarly for TM modes :  
    
-$`\overrightarrow{E}_{\parallel}=
-\left(\begin{array}{l}
+$`\overrightarrow{E}_{\parallel}=`$
+$`\left(\begin{array}{l}
 0\\
-2\,E_0\,\sin\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\cdot z \cdot \sin\,\theta-\omega t)\\
--2\,E_0\,\cos\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\cdot z \cdot \sin\,\theta-\omega t)
+2\,E_0\,\sin\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\,\sinc\,\theta\;z -\omega t)\\
+-2\,E_0\,\cos\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\,\sinc\,\theta\;z -\omega t)
 \end{array}\right)`$    
    
 and   
    
 $`\overrightarrow{B}_{\parallel}=\underbrace{-2\,E_0\,\sin(k\cdot y\cdot \cos\,\theta)}_{\large{amplitude}}
-\times \sin\big(\underbrace{k\,\sin\,\theta}_{\large{wavevector}}\;z-\omega t\big)\overrightarrow{e_z}`$ 
+\times \sin\big(\underbrace{k\,\sin\,\theta}_{\large{wavevector}}\,z-\omega t\big)\overrightarrow{e_z}`$