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Display information for equation id:math.2152.28 on revision:2152
* Page found: Grenzbedingungen für Felder (eq math.2152.28)
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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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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo>=</mo><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>D</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo>=</mo><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>D</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo>⇒</mo><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo>=</mo><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi>tan</mi><mo>⁡</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></msup></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mi>tan</mi><mo>⁡</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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