Update textbook.fr.md

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

@@ -26,26 +26,26 @@ _TE and TM waves and their corresponding standing wave behaviour along the y axi
    
 $`\overrightarrow{E}_{\perp}=\underbrace{-2\,E_0\,\sin(k\cdot y\cdot \cos\,\theta)}_{\large{amplitude}}
 \times \sin\big(\underbrace{k\,\sin\,\theta}_{\large{wavevector}}\,z-\omega t\big)\overrightarrow{e_z}`$    
-   
-<br>
+
    
 $`\overrightarrow{B}_{\perp}=`$
 $`\left(\begin{array}{l}
 0\\
--\dfrac{2\,E_0}{c}\sin\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\,\sinc\,\theta\;z -\omega t)\\
--\dfrac{2\,E_0}{c}\cos\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\,\sinc\,\theta\;z -\omega t)
+-\dfrac{2\,E_0}{c}\sin\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\,\sin\,\theta\;z -\omega t)\\
+-\dfrac{2\,E_0}{c}\cos\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\,\sin\,\theta\;z -\omega t)
 \end{array}\right)`$
 
+<br>
+
 * Similarly for TM modes :  
    
 $`\overrightarrow{E}_{\parallel}=`$
 $`\left(\begin{array}{l}
 0\\
-2\,E_0\,\sin\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\,\sinc\,\theta\;z -\omega t)\\
--2\,E_0\,\cos\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\,\sinc\,\theta\;z -\omega t)
+2\,E_0\,\sin\,\theta \,\cos\,(k\cdot y \cdot \cos\,\theta)\,\cos\,(k\,\sin\,\theta\;z -\omega t)\\
+-2\,E_0\,\cos\,\theta \,\sin\,(k\cdot y \cdot \cos\,\theta)\,\sin\,(k\,\sin\,\theta\;z -\omega t)
 \end{array}\right)`$    
    
-and   
    
 $`\overrightarrow{B}_{\parallel}=\underbrace{-2\,E_0\,\sin(k\cdot y\cdot \cos\,\theta)}_{\large{amplitude}}
 \times \sin\big(\underbrace{k\,\sin\,\theta}_{\large{wavevector}}\,z-\omega t\big)\overrightarrow{e_z}`$