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Maxwell's Equations

Maxwell's equations are a set of four equations that govern electricity and magnetism in physics.

They are as follows:

  • $\oiint \mathbf{E} \cdot d\mathbf{A} = \frac{q_{enc}}{\varepsilon_0}$ (Gauss's law of electricity),
  • $\oiint \mathbf{B} \cdot d\mathbf{A} = 0$ (Gauss's law of magnetism),
  • $\oint \mathbf{E} \cdot d\mathbf{\ell} = -\frac{d}{dt} \iint \mathbf{B} \cdot d\mathbf{A}$ (Faraday's law),
  • $\oint \mathbf{B} \cdot d\mathbf{\ell} = \mu_0I + \mu_0\varepsilon_0 \frac{d}{dt}\iint \mathbf{E} \cdot d\mathbf{A}$ (Ampere's law).

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