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Display information for equation id:math.1444.152 on revision:1444

* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.152)

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Hash: 0c48aa0cc2d36b1d45faa6ba1ca35648

TeX (original user input):

\begin{align}
& {{{\bar{E}}}_{t}}^{(1)}={{{\bar{E}}}_{t}}^{(2)} \\
& {{{\bar{D}}}_{n}}^{(1)}={{{\bar{D}}}_{n}}^{(2)}\Rightarrow {{\varepsilon }_{1}}{{{\bar{E}}}_{n}}^{(1)}={{\varepsilon }_{2}}{{{\bar{E}}}_{n}}^{(2)} \\
& \Rightarrow {{{\bar{E}}}_{n}}^{(2)}=\frac{{{\varepsilon }_{1}}}{{{\varepsilon }_{2}}}{{{\bar{E}}}_{n}}^{(1)} \\
& \tan {{\alpha }_{1}}=\frac{{{{\bar{E}}}_{t}}^{(1)}}{{{{\bar{E}}}_{n}}^{(1)}}=\frac{{{\varepsilon }_{1}}}{{{\varepsilon }_{2}}}\frac{{{{\bar{E}}}_{t}}^{(2)}}{{{{\bar{E}}}_{n}}^{(2)}}=\frac{{{\varepsilon }_{1}}}{{{\varepsilon }_{2}}}\tan {{\alpha }_{2}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\bar {E}}_{t}}^{(1)}={{\bar {E}}_{t}}^{(2)}\\&{{\bar {D}}_{n}}^{(1)}={{\bar {D}}_{n}}^{(2)}\Rightarrow {{\varepsilon }_{1}}{{\bar {E}}_{n}}^{(1)}={{\varepsilon }_{2}}{{\bar {E}}_{n}}^{(2)}\\&\Rightarrow {{\bar {E}}_{n}}^{(2)}={\frac {{\varepsilon }_{1}}{{\varepsilon }_{2}}}{{\bar {E}}_{n}}^{(1)}\\&\tan {{\alpha }_{1}}={\frac {{{\bar {E}}_{t}}^{(1)}}{{{\bar {E}}_{n}}^{(1)}}}={\frac {{\varepsilon }_{1}}{{\varepsilon }_{2}}}{\frac {{{\bar {E}}_{t}}^{(2)}}{{{\bar {E}}_{n}}^{(2)}}}={\frac {{\varepsilon }_{1}}{{\varepsilon }_{2}}}\tan {{\alpha }_{2}}\\\end{aligned}}

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MathML (44.736 KB / 4.496 KB) :

E ¯ t ( 1 ) = E ¯ t ( 2 ) D ¯ n ( 1 ) = D ¯ n ( 2 ) ε 1 E ¯ n ( 1 ) = ε 2 E ¯ n ( 2 ) E ¯ n ( 2 ) = ε 1 ε 2 E ¯ n ( 1 ) tan α 1 = E ¯ t ( 1 ) E ¯ n ( 1 ) = ε 1 ε 2 E ¯ t ( 2 ) E ¯ n ( 2 ) = ε 1 ε 2 tan α 2 missing-subexpression superscript subscript ¯ 𝐸 𝑡 1 superscript subscript ¯ 𝐸 𝑡 2 missing-subexpression superscript subscript ¯ 𝐷 𝑛 1 superscript subscript ¯ 𝐷 𝑛 2 subscript 𝜀 1 superscript subscript ¯ 𝐸 𝑛 1 subscript 𝜀 2 superscript subscript ¯ 𝐸 𝑛 2 missing-subexpression absent superscript subscript ¯ 𝐸 𝑛 2 subscript 𝜀 1 subscript 𝜀 2 superscript subscript ¯ 𝐸 𝑛 1 missing-subexpression subscript 𝛼 1 superscript subscript ¯ 𝐸 𝑡 1 superscript subscript ¯ 𝐸 𝑛 1 subscript 𝜀 1 subscript 𝜀 2 superscript subscript ¯ 𝐸 𝑡 2 superscript subscript ¯ 𝐸 𝑛 2 subscript 𝜀 1 subscript 𝜀 2 subscript 𝛼 2 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{{\bar{E}}}_{t}}^{(% 1)}={{{\bar{E}}}_{t}}^{(2)}\\ &\displaystyle{{{\bar{D}}}_{n}}^{(1)}={{{\bar{D}}}_{n}}^{(2)}\Rightarrow{{% \varepsilon}_{1}}{{{\bar{E}}}_{n}}^{(1)}={{\varepsilon}_{2}}{{{\bar{E}}}_{n}}^% {(2)}\\ &\displaystyle\Rightarrow{{{\bar{E}}}_{n}}^{(2)}=\frac{{{\varepsilon}_{1}}}{{{% \varepsilon}_{2}}}{{{\bar{E}}}_{n}}^{(1)}\\ &\displaystyle\tan{{\alpha}_{1}}=\frac{{{{\bar{E}}}_{t}}^{(1)}}{{{{\bar{E}}}_{% n}}^{(1)}}=\frac{{{\varepsilon}_{1}}}{{{\varepsilon}_{2}}}\frac{{{{\bar{E}}}_{% t}}^{(2)}}{{{{\bar{E}}}_{n}}^{(2)}}=\frac{{{\varepsilon}_{1}}}{{{\varepsilon}_% {2}}}\tan{{\alpha}_{2}}\\ \end{aligned}}}

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MathML (5.83 KB / 488 B) :

E¯t(1)=E¯t(2)D¯n(1)=D¯n(2)ε1E¯n(1)=ε2E¯n(2)E¯n(2)=ε1ε2E¯n(1)tanα1=E¯t(1)E¯n(1)=ε1ε2E¯t(2)E¯n(2)=ε1ε2tanα2

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Calculated based on the variables occurring on the entire Materie in elektrischen und magnetischen Feldern page

Identifiers

  • E¯t
  • E¯t
  • D¯n
  • D¯n
  • ε1
  • E¯n
  • ε2
  • E¯n
  • E¯n
  • ε1
  • ε2
  • E¯n
  • α1
  • E¯t
  • E¯n
  • ε1
  • ε2
  • E¯t
  • E¯n
  • ε1
  • ε2
  • α2

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