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Display information for equation id:math.2062.5 on revision:2062

* Page found: Kontinuitätsgleichung (eq math.2062.5)

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\Rightarrow \frac{d}{dt}\int_{V}^{{}}{{}}{{d}^{3}}r\rho (\bar{r},t)=-\oint\limits_{\partial V}{{}}d\bar{f}\bar{j}(\bar{r},t)=-\int_{V}^{{}}{{{d}^{3}}r}\nabla \cdot \bar{j}(\bar{r},t)

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⇒ d d ⁢ t ⁢ ∫ V d 3 ⁢ r ⁢ ρ ⁢ ( r ¯ , t ) = - ∮ ∂ ⁡ V 𝑑 f ¯ ⁢ j ¯ ⁢ ( r ¯ , t ) = - ∫ V d 3 ⁢ r ⁢ ∇ ⋅ j ¯ ⁢ ( r ¯ , t ) ⇒ absent 𝑑 𝑑 𝑡 subscript 𝑉 superscript 𝑑 3 𝑟 𝜌 ¯ 𝑟 𝑡 subscript contour-integral 𝑉 differential-d ¯ 𝑓 ¯ 𝑗 ¯ 𝑟 𝑡 subscript 𝑉 ⋅ superscript 𝑑 3 𝑟 ∇ ¯ 𝑗 ¯ 𝑟 𝑡 {\displaystyle{\displaystyle\Rightarrow\frac{d}{dt}\int_{V}{{}}{{d}^{3}}r\rho(% \bar{r},t)=-\oint\limits_{\partial V}{{}}d\bar{f}\bar{j}(\bar{r},t)=-\int_{V}{% {{d}^{3}}r}\nabla\cdot\bar{j}(\bar{r},t)}}

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⇒ddt∫Vd3rρ(r¯,t)=−∮∂Vdf¯j¯(r¯,t)=−∫Vd3r∇⋅j¯(r¯,t)

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