Update textbook.fr.md

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

@@ -21,70 +21,36 @@ Before considering the reflection and transmission of electromagnetic
 waves between two media, we have to determine the relations governing
 the be- haviour of the fields $`\overrightarrow{D}`$, $`\overrightarrow{B}`$, $`\overrightarrow{E}`$ and $`\overrightarrow{H}`$ at the
 interface between two materials. Simply stated, these relations,
-called the "*boundary conditions*" tell us that if we know the fields
+called the "__boundary conditions__" tell us that if we know the fields
 in one material close to the separation surface then we can calculate
 some components of these same fields in the other material (again,
 close to the separation surface). We will consider an LHI material and
-the relations we will find are valid **for any point** close to the
-separation surface and **for any time**. These two conditions are
+the relations we will find are valid __for any point__ close to the
+separation surface and __for any time__. These two conditions are
 important to find some of the results later in this chapter. The
 boundary conditions can be obtained from the Maxwell equations. The
 first two equations
 
-i.  tS
-
-$`\overrightarrow{D}`$ · *d*$`\overrightarrow{S}`$ = *Q^encl.^*
->
-(3.1)
-
-ii. tS $`\overrightarrow{B}`$ · *d*$`\overrightarrow{S}`$ = 0 (3.2)
-
-(3.3)
+@@@@@@@@@@@@
 
 will give information on the normal components of $`\overrightarrow{D}`$ and $`\overrightarrow{B}`$,
 while the third and fourth
 
-iii. t $`\overrightarrow{E}`$ · *d***l** = − [d]{.underline} { $`\overrightarrow{B}`$ · *d*$`\overrightarrow{S}`$ (3.4)
-
-iv. t $`\overrightarrow{H}`$ · *d***l** = *I^encl.^* + [d]{.underline} { $`\overrightarrow{D}`$ · *d*$`\overrightarrow{S}`$
-    (3.5)
-
-~C~ d*t* ~S~
-
-(3.6)
+@@@@@@@@@@@@
 
 will give information on the tangential components of $`\overrightarrow{E}`$ and $`\overrightarrow{H}`$.
 >
 To obtain the boundary conditions we consider a surface separating two
-Linear 49
-
-![](media/image167.jpeg)nˆ2 1 cylinder
-
-boundary 1
-
-medium 1
-
-medium 2
+Linear Homogeneous and Isotropic (LHI) media whose properties such as that
+the permittivity and permeability are different. We denote as
+$`\overrightarrow{E}_1\,,\overrightarrow{B}_1\,,\overrightarrow{D}_1`$ and $`\overrightarrow{H}_1`$ the fields present in
+material 1 close to its surface. Likewise an index 2 will be used for
+the fields in the second material.
 
-da~2~
->
-nˆ~1~ ~2~
->
-(J\'*~s~*
->
-top, bottom and middle surfaces
->
-of the box used to calculate the flux
->
 Figure 3.1: []{#_bookmark59 .anchor}Scheme for deriving boundary
 conditions for perpendicular field components. S~1~, S~2~ and S^t^
 represent respectively the surface at the top, bot- tom and interface.
 >
-Homogeneous and Isotropic (LHI) media whose properties such as that
-the permittivity and permeability are different. We denote as
-$`\overrightarrow{E}`$~1~, $`\overrightarrow{B}`$~1~, $`\overrightarrow{D}`$~1~ and $`\overrightarrow{H}`$~1~ the fields present in
-material 1 close to its surface. Likewise an index 2 will be used for
-the fields in the second material.
 
 __**Normal components**__