so my book has a point charge q inside an arbitrary surface S and at a point P on the surface S, the electric field is E = q/4(π)(ε(adsbygoogle = window.adsbygoogle || []).push({}); _{0})(r^{2}). so the flux through S is then dΦ = E * dS = q/4(π)(ε_{0})(r^{2}) * dS = q/4(π)(ε_{0}) * dScosθ /(r^{2}) = q/4(π)(ε_{0}) * dΩ. then my book takes the integral of both sides and ends up with Φ = q/4(π)(ε_{0}) ∫ dΩ = q/4(π)(ε_{0}) (4π) = q/(ε_{0}).

what i don't understand it how did ∫ dΩ become 4π?

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# Proof of Gauss's law using coulomb's law

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