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Display information for equation id:math.2118.0 on revision:2118

* Page found: Impulsbilanz (eq math.2118.0)

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\begin{align}
& \frac{\partial }{\partial t}\left( \bar{D}\times \bar{B} \right)=\dot{\bar{D}}\times \bar{B}+\bar{D}\times \dot{\bar{B}} \\
& \dot{\bar{D}}=\nabla \times \bar{H}-\bar{j} \\
& \dot{\bar{B}}=-\nabla \times \bar{E} \\
& \Rightarrow \frac{\partial }{\partial t}\left( \bar{D}\times \bar{B} \right)=-\frac{1}{{{\mu }_{0}}}\bar{B}\times \left( \nabla \times \bar{B} \right)-\bar{j}\times \bar{B}-{{\varepsilon }_{o}}\bar{E}\times \left( \nabla \times \bar{E} \right) \\
\end{align}

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∂ ∂ ⁡ t ⁢ ( D ¯ × B ¯ ) = D ¯ ˙ × B ¯ + D ¯ × B ¯ ˙ D ¯ ˙ = ∇ × H ¯ - j ¯ B ¯ ˙ = - ∇ × E ¯ ⇒ ∂ ∂ ⁡ t ⁢ ( D ¯ × B ¯ ) = - 1 μ 0 ⁢ B ¯ × ( ∇ × B ¯ ) - j ¯ × B ¯ - ε o ⁢ E ¯ × ( ∇ × E ¯ ) missing-subexpression 𝑡 ¯ 𝐷 ¯ 𝐵 ˙ ¯ 𝐷 ¯ 𝐵 ¯ 𝐷 ˙ ¯ 𝐵 missing-subexpression ˙ ¯ 𝐷 ∇ ¯ 𝐻 ¯ 𝑗 missing-subexpression ˙ ¯ 𝐵 ∇ ¯ 𝐸 missing-subexpression ⇒ absent 𝑡 ¯ 𝐷 ¯ 𝐵 1 subscript 𝜇 0 ¯ 𝐵 ∇ ¯ 𝐵 ¯ 𝑗 ¯ 𝐵 subscript 𝜀 𝑜 ¯ 𝐸 ∇ ¯ 𝐸 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\frac{\partial}{% \partial t}\left(\bar{D}\times\bar{B}\right)=\dot{\bar{D}}\times\bar{B}+\bar{D% }\times\dot{\bar{B}}\\ &\displaystyle\dot{\bar{D}}=\nabla\times\bar{H}-\bar{j}\\ &\displaystyle\dot{\bar{B}}=-\nabla\times\bar{E}\\ &\displaystyle\Rightarrow\frac{\partial}{\partial t}\left(\bar{D}\times\bar{B}% \right)=-\frac{1}{{{\mu}_{0}}}\bar{B}\times\left(\nabla\times\bar{B}\right)-% \bar{j}\times\bar{B}-{{\varepsilon}_{o}}\bar{E}\times\left(\nabla\times\bar{E}% \right)\\ \end{aligned}}}

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∂∂t(D¯×B¯)=D¯˙×B¯+D¯×B¯˙D¯˙=∇×H¯−j¯B¯˙=−∇×E¯⇒∂∂t(D¯×B¯)=−1μ0B¯×(∇×B¯)−j¯×B¯−εoE¯×(∇×E¯)

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