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/ee/ - Electrical Engineering

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25 Dec 2021	Mathchan is launched into public

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File: james maxwell.jpg ( 15.97 KB , 300x300 , 1641415993367.jpg )

Maxwell's equations Anonymous January 05, 2022 (Wed) 20:53:13 No. 4

Gauss's law

\qquad \oiint_{\partial\Omega}\textbf{E}\cdot\textrm{d}\textbf{S} = \frac{1}{\varepsilon_0}\iiint_\Omega\rho\,\mathrm{d}V

Gauss's law for magnetism

\qquad \oiint_{\partial\Omega}\textbf{B}\cdot\textrm{d}\textbf{S} = 0

Faraday's law

\qquad \oint_{\partial\Sigma}\textbf{E}\cdot\textrm{d}\ell = -\frac{\textrm{d}}{\textrm{d}t}\iint_\Sigma\textbf{B}\cdot\textrm{d}\textbf{S}

Ampere's law

\qquad \oint_{\partial\Sigma}\textbf{B}\cdot\textrm{d}\ell = \mu_0\left(\iint_\Sigma\textbf{J}\cdot\textrm{d}\textbf{S} + \varepsilon_0\frac{\textrm{d}}{\textrm{d}t}\iint_\Sigma\textbf{E}\cdot\textrm{d}\textbf{S}\right)

Anonymous January 05, 2022 (Wed) 21:00:30 No. 5

In differential form:

\begin{aligned} \nabla\cdot\textbf{E} &= {\rho \over \varepsilon_0}\\ \nabla\cdot\textbf{B} &= 0\\ \nabla\times\textbf{E} &= -\frac{\partial\textbf{B}}{\partial t}\\ \nabla\times\textbf{B}&=\mu_0\left(\textbf{J} + \varepsilon_0\frac{\partial\textbf{E}}{\partial t}\right) \end{aligned}

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