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Display information for equation id:math.1444.213 on revision:1444

* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.213)

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Hash: 2b5699358178d343477a7dd31138de17

TeX (original user input): 

\begin{align}
& {{\left( \nabla \times \bar{E} \right)}_{2}}=\frac{\partial {{E}_{1}}}{\partial {{x}_{3}}}=-{{{\dot{B}}}_{2}} \\
& \Leftrightarrow i\frac{\omega }{c}\left( n+i\gamma  \right){{E}_{1}}=i\omega {{B}_{2}} \\
& \Leftrightarrow {{B}_{2}}=\frac{\left( n+i\gamma  \right)}{c}{{E}_{1}}=\frac{\sqrt{{{n}^{2}}+{{\gamma }^{2}}}}{c}{{e}^{i\phi }}{{E}_{1}} \\
\end{align}

TeX (checked): 

{\begin{aligned}&{{\left(\nabla \times {\bar {E}}\right)}_{2}}={\frac {\partial {{E}_{1}}}{\partial {{x}_{3}}}}=-{{\dot {B}}_{2}}\\&\Leftrightarrow i{\frac {\omega }{c}}\left(n+i\gamma \right){{E}_{1}}=i\omega {{B}_{2}}\\&\Leftrightarrow {{B}_{2}}={\frac {\left(n+i\gamma \right)}{c}}{{E}_{1}}={\frac {\sqrt {{{n}^{2}}+{{\gamma }^{2}}}}{c}}{{e}^{i\phi }}{{E}_{1}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (27.724 KB / 3.281 KB) :

( ∇ × E ¯ ) 2 = ∂ ⁡ E 1 ∂ ⁡ x 3 = - B ˙ 2 ⇔ i ⁢ ω c ⁢ ( n + i ⁢ γ ) ⁢ E 1 = i ⁢ ω ⁢ B 2 ⇔ B 2 = ( n + i ⁢ γ ) c ⁢ E 1 = n 2 + γ 2 c ⁢ e i ⁢ ϕ ⁢ E 1 missing-subexpression subscript ∇ ¯ 𝐸 2 subscript 𝐸 1 subscript 𝑥 3 subscript ˙ 𝐵 2 missing-subexpression ⇔ absent 𝑖 𝜔 𝑐 𝑛 𝑖 𝛾 subscript 𝐸 1 𝑖 𝜔 subscript 𝐵 2 missing-subexpression ⇔ absent subscript 𝐵 2 𝑛 𝑖 𝛾 𝑐 subscript 𝐸 1 superscript 𝑛 2 superscript 𝛾 2 𝑐 superscript 𝑒 𝑖 italic-ϕ subscript 𝐸 1 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle{{\left(\nabla\times% \bar{E}\right)}_{2}}=\frac{\partial{{E}_{1}}}{\partial{{x}_{3}}}=-{{{\dot{B}}}% _{2}}\\ &\displaystyle\Leftrightarrow i\frac{\omega}{c}\left(n+i\gamma\right){{E}_{1}}% =i\omega{{B}_{2}}\\ &\displaystyle\Leftrightarrow{{B}_{2}}=\frac{\left(n+i\gamma\right)}{c}{{E}_{1% }}=\frac{\sqrt{{{n}^{2}}+{{\gamma}^{2}}}}{c}{{e}^{i\phi}}{{E}_{1}}\\ \end{aligned}}}

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MathML (2.929 KB / 547 B) :

(∇×E¯)2=∂E1∂x3=−B˙2⇔iωc(n+iγ)E1=iωB2⇔B2=(n+iγ)cE1=n2+γ2ceiϕE1

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

Identifiers

  • E¯2
  • E1
  • x3
  • B˙2
  • i
  • ω
  • c
  • n
  • i
  • γ
  • E1
  • i
  • ω
  • B2
  • B2
  • n
  • i
  • γ
  • c
  • E1
  • n
  • γ
  • c
  • e
  • i
  • ϕ
  • E1

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