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* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.198)

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TeX (original user input): 

\begin{align}
& \rho =0 \\
& \nabla \times \bar{E}+\dot{\bar{B}}=0 \\
& \nabla \times \bar{B}-{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}\dot{\bar{E}}={{\mu }_{0}}\mu \bar{j}={{\mu }_{0}}\mu \sigma \bar{E} \\
& \nabla \cdot \bar{E}=0 \\
& \nabla \cdot \bar{B}=0 \\
& \Rightarrow \nabla \times \left( \nabla \times \bar{E} \right)=\nabla \left( \nabla \cdot \bar{E} \right)-\Delta \bar{E}=-\Delta \bar{E}=-\nabla \times \dot{\bar{B}}=-{{\mu }_{0}}\mu \sigma \dot{\bar{E}}-{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}\ddot{\bar{E}} \\
&  \\
& \Delta \bar{E}={{\mu }_{0}}\mu \sigma \dot{\bar{E}}+{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}\ddot{\bar{E}} \\
\end{align}

TeX (checked): 

{\begin{aligned}&\rho =0\\&\nabla \times {\bar {E}}+{\dot {\bar {B}}}=0\\&\nabla \times {\bar {B}}-{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}{\dot {\bar {E}}}={{\mu }_{0}}\mu {\bar {j}}={{\mu }_{0}}\mu \sigma {\bar {E}}\\&\nabla \cdot {\bar {E}}=0\\&\nabla \cdot {\bar {B}}=0\\&\Rightarrow \nabla \times \left(\nabla \times {\bar {E}}\right)=\nabla \left(\nabla \cdot {\bar {E}}\right)-\Delta {\bar {E}}=-\Delta {\bar {E}}=-\nabla \times {\dot {\bar {B}}}=-{{\mu }_{0}}\mu \sigma {\dot {\bar {E}}}-{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}{\ddot {\bar {E}}}\\&\\&\Delta {\bar {E}}={{\mu }_{0}}\mu \sigma {\dot {\bar {E}}}+{{\mu }_{0}}\mu \varepsilon {{\varepsilon }_{0}}{\ddot {\bar {E}}}\\\end{aligned}}

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MathML (49.316 KB / 5.134 KB) :

ρ = 0 ∇ × E ¯ + B ¯ ˙ = 0 ∇ × B ¯ - μ 0 ⁢ μ ⁢ ε ⁢ ε 0 ⁢ E ¯ ˙ = μ 0 ⁢ μ ⁢ j ¯ = μ 0 ⁢ μ ⁢ σ ⁢ E ¯ ∇ ⋅ E ¯ = 0 ∇ ⋅ B ¯ = 0 ⇒ ∇ × ( ∇ × E ¯ ) = ∇ ⁡ ( ∇ ⋅ E ¯ ) - Δ ⁢ E ¯ = - Δ ⁢ E ¯ = - ∇ × B ¯ ˙ = - μ 0 ⁢ μ ⁢ σ ⁢ E ¯ ˙ - μ 0 ⁢ μ ⁢ ε ⁢ ε 0 ⁢ E ¯ ¨ Δ ⁢ E ¯ = μ 0 ⁢ μ ⁢ σ ⁢ E ¯ ˙ + μ 0 ⁢ μ ⁢ ε ⁢ ε 0 ⁢ E ¯ ¨ missing-subexpression 𝜌 0 missing-subexpression ∇ ¯ 𝐸 ˙ ¯ 𝐵 0 missing-subexpression ∇ ¯ 𝐵 subscript 𝜇 0 𝜇 𝜀 subscript 𝜀 0 ˙ ¯ 𝐸 subscript 𝜇 0 𝜇 ¯ 𝑗 subscript 𝜇 0 𝜇 𝜎 ¯ 𝐸 missing-subexpression ⋅ ∇ ¯ 𝐸 0 missing-subexpression ⋅ ∇ ¯ 𝐵 0 missing-subexpression ⇒ absent ∇ ∇ ¯ 𝐸 ∇ ⋅ ∇ ¯ 𝐸 Δ ¯ 𝐸 Δ ¯ 𝐸 ∇ ˙ ¯ 𝐵 subscript 𝜇 0 𝜇 𝜎 ˙ ¯ 𝐸 subscript 𝜇 0 𝜇 𝜀 subscript 𝜀 0 ¨ ¯ 𝐸 missing-subexpression missing-subexpression missing-subexpression Δ ¯ 𝐸 subscript 𝜇 0 𝜇 𝜎 ˙ ¯ 𝐸 subscript 𝜇 0 𝜇 𝜀 subscript 𝜀 0 ¨ ¯ 𝐸 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\rho=0\\ &\displaystyle\nabla\times\bar{E}+\dot{\bar{B}}=0\\ &\displaystyle\nabla\times\bar{B}-{{\mu}_{0}}\mu\varepsilon{{\varepsilon}_{0}}% \dot{\bar{E}}={{\mu}_{0}}\mu\bar{j}={{\mu}_{0}}\mu\sigma\bar{E}\\ &\displaystyle\nabla\cdot\bar{E}=0\\ &\displaystyle\nabla\cdot\bar{B}=0\\ &\displaystyle\Rightarrow\nabla\times\left(\nabla\times\bar{E}\right)=\nabla% \left(\nabla\cdot\bar{E}\right)-\Delta\bar{E}=-\Delta\bar{E}=-\nabla\times\dot% {\bar{B}}=-{{\mu}_{0}}\mu\sigma\dot{\bar{E}}-{{\mu}_{0}}\mu\varepsilon{{% \varepsilon}_{0}}\ddot{\bar{E}}\\ &\\ &\displaystyle\Delta\bar{E}={{\mu}_{0}}\mu\sigma\dot{\bar{E}}+{{\mu}_{0}}\mu% \varepsilon{{\varepsilon}_{0}}\ddot{\bar{E}}\\ \end{aligned}}}

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MathML (5.349 KB / 535 B) :

ρ=0∇×E¯+B¯˙=0∇×B¯−μ0μεε0E¯˙=μ0μj¯=μ0μσE¯∇⋅E¯=0∇⋅B¯=0⇒∇×(∇×E¯)=∇(∇⋅E¯)−ΔE¯=−ΔE¯=−∇×B¯˙=−μ0μσE¯˙−μ0μεε0E¯¨ΔE¯=μ0μσE¯˙+μ0μεε0E¯¨

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  • ρ
  • E¯
  • B¯˙
  • B¯
  • μ0
  • μ
  • ε
  • ε0
  • E¯˙
  • μ0
  • μ
  • j¯
  • μ0
  • μ
  • σ
  • E¯
  • E¯
  • B¯
  • E¯
  • E¯
  • Δ
  • E¯
  • Δ
  • E¯
  • B¯˙
  • μ0
  • μ
  • σ
  • E¯˙
  • μ0
  • μ
  • ε
  • ε0
  • E¯¨
  • Δ
  • E¯
  • μ0
  • μ
  • σ
  • E¯˙
  • μ0
  • μ
  • ε
  • ε0
  • E¯¨

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