Maxwell's Equations

All of electromagnetism can be condensed into these four equations, known as Maxwell’s equations, along with the Lorentz Force.

Gauss’ Law §

Gauss Law for Magnetic Fields §

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Faraday’s Law §

Ampère-Maxwell Law §

We can also combine all 4 equations to form two equations:

$$\oint {\vec{E}}_{ind}\cdot d\vec{l}=-\frac{\text{d}}{\text{d}t}\left(\oint \vec{B}\cdot \text{d}\vec{A}\right)$$

$$\oint \vec{B}\cdot d\vec{l}={\mu }_0\left(I+{ϵ}_0\frac{\text{d}}{\text{d}t}(\oint \vec{E}\cdot d\vec{A})\right)$$