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Display information for equation id:math.2174.38 on revision:2174

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Transformationsverhalten der Ströme und Felder Eq: math.2174.38

Hash: 9479d079644d13562128ffb315aaf47c

TeX (original user input):

\begin{align}
& {{E}^{1}}\acute{\ }={{E}^{1}} \\
& {{E}^{2}}\acute{\ }=\frac{1}{\sqrt{1-{{\beta }^{2}}}}\left( {{E}^{2}}-v{{B}^{3}} \right) \\
& {{E}^{3}}\acute{\ }=\frac{1}{\sqrt{1-{{\beta }^{2}}}}\left( {{E}^{3}}+v{{B}^{2}} \right) \\
& {{B}^{1}}\acute{\ }={{B}^{1}} \\
& {{B}^{2}}\acute{\ }=\frac{1}{\sqrt{1-{{\beta }^{2}}}}\left( {{B}^{2}}+\frac{v}{{{c}^{2}}}{{E}^{3}} \right) \\
& {{B}^{3}}\acute{\ }=\frac{1}{\sqrt{1-{{\beta }^{2}}}}\left( {{B}^{3}}-\frac{v}{{{c}^{2}}}{{E}^{2}} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&{{E}^{1}}{\acute {\ }}={{E}^{1}}\\&{{E}^{2}}{\acute {\ }}={\frac {1}{\sqrt {1-{{\beta }^{2}}}}}\left({{E}^{2}}-v{{B}^{3}}\right)\\&{{E}^{3}}{\acute {\ }}={\frac {1}{\sqrt {1-{{\beta }^{2}}}}}\left({{E}^{3}}+v{{B}^{2}}\right)\\&{{B}^{1}}{\acute {\ }}={{B}^{1}}\\&{{B}^{2}}{\acute {\ }}={\frac {1}{\sqrt {1-{{\beta }^{2}}}}}\left({{B}^{2}}+{\frac {v}{{c}^{2}}}{{E}^{3}}\right)\\&{{B}^{3}}{\acute {\ }}={\frac {1}{\sqrt {1-{{\beta }^{2}}}}}\left({{B}^{3}}-{\frac {v}{{c}^{2}}}{{E}^{2}}\right)\\\end{aligned}}

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\begin{matrix} E^{1} \overset{´}{} = E^{1} \\ E^{2} \overset{´}{} = \frac{1}{\sqrt{1 - β^{2}}} (E^{2} - v B^{3}) \\ E^{3} \overset{´}{} = \frac{1}{\sqrt{1 - β^{2}}} (E^{3} + v B^{2}) \\ B^{1} \overset{´}{} = B^{1} \\ B^{2} \overset{´}{} = \frac{1}{\sqrt{1 - β^{2}}} (B^{2} + \frac{v}{c^{2}} E^{3}) \\ B^{3} \overset{´}{} = \frac{1}{\sqrt{1 - β^{2}}} (B^{3} - \frac{v}{c^{2}} E^{2}) \end{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">−</mo><mi>v</mi><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo stretchy="false">+</mo><mi>v</mi><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$E$

$\overset{´}{}$

$E$

$E$

$\overset{´}{}$

$β$

$E$

$v$

$B$

$E$

$\overset{´}{}$

$β$

$E$

$v$

$B$

$B$

$\overset{´}{}$

$B$

$B$

$\overset{´}{}$

$β$

$B$

$v$

$c$

$E$

$B$

$\overset{´}{}$

$β$

$B$

$v$

$c$

$E$

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