Maxwell’s equations

Gauß’s Law for Electric Flux

Gauß’s law states that the number of field lines passing through the surface of a solid Ω (the electric flux) is proportional to the charge enclosed within.

Φ=⊂⊃∬𝜕Ω⃗𝐄⋅𝑑⃗𝐚=𝑄enc𝜖0=1𝜖0∭Ω𝜌𝑑𝜏′

Using Острогра́дский’s divergence theorem, we see

⃗∇⋅⃗𝐄=𝜌𝜖0

See also Gauß’s law for diëlectrics.

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