Maxwell Equations Integral

Tags: #physics #maxwell #electricity #magnetism


$$\oiint (\vec{D}\cdot \vec{n}) \mathrm{d}^{2}A=Q_{\text{free,included}}\\ \oiint (\vec{B}\cdot \vec{n}) \mathrm{d}^{2}A=0 \\ \oint \vec{E} \mathrm{d}\vec{s}=-\frac{\mathrm{d}\Phi}{\mathrm{d}t}\\ \oint \vec{H} \mathrm{d}\vec{s}=I_{\text{free,included}}+\frac{\mathrm{d}\Psi }{\mathrm{d}t}$$

Latex Code

                                 \oiint (\vec{D}\cdot \vec{n}) \mathrm{d}^{2}A=Q_{\text{free,included}}\\ 
            \oiint (\vec{B}\cdot \vec{n}) \mathrm{d}^{2}A=0 \\ 
            \oint \vec{E} \mathrm{d}\vec{s}=-\frac{\mathrm{d}\Phi}{\mathrm{d}t}\\ 
            \oint \vec{H} \mathrm{d}\vec{s}=I_{\text{free,included}}+\frac{\mathrm{d}\Psi }{\mathrm{d}t}

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Latex code for integral form of the Maxwell Equations. I will briefly introduce the notations in this formulation.

  • : The electric displacement
  • : The electric field strength
  • : The magnetic flux density
  • : The magnetic field strength
  • In the formulation, the first formula (1) describes the property of electric displacement . The second formula (2) describes the property of magnetic flux density . The third formula (3) describes how the variation in magnetic flux density influence the electric field strength . The fourth formula (4) describes how the variation in electric displacement influence the magnetic field strength .

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