Gauss's law in integral form is expressed as which of the following?

Gauss's law in integral form is expressed as which of the following?

• A. ∮ E · dA = Q_enclosed / ε0
• B. ∮ E · dA = ε0 / Q_enclosed
• C. ∮ E · dA = Q_enclosed
• D. ∮ E · dA = ε0 Q_enclosed

Answer: (A)

Electric flux through a closed surface is given by the surface integral ∮ E · dA, where dA is the outward-directed area element. Gauss's law in integral form states that this flux equals the amount of charge enclosed by the surface divided by the vacuum permittivity ε0. So the relationship is ∮ E · dA = Q_enclosed / ε0. The outward orientation of dA matters: positive enclosed charge produces a net outward flux, negative enclosed charge yields inward flux. The units also line up, since ε0 carries units that convert the flux into units of charge. In differential form, Gauss's law is ∇·E = ρ/ε0, tying the local divergence of E to the local charge density.

Electric flux through a closed surface is given by the surface integral ∮ E · dA, where dA is the outward-directed area element. Gauss's law in integral form states that this flux equals the amount of charge enclosed by the surface divided by the vacuum permittivity ε0. So the relationship is ∮ E · dA = Q_enclosed / ε0. The outward orientation of dA matters: positive enclosed charge produces a net outward flux, negative enclosed charge yields inward flux. The units also line up, since ε0 carries units that convert the flux into units of charge. In differential form, Gauss's law is ∇·E = ρ/ε0, tying the local divergence of E to the local charge density.