According to Gauss's law, the electric flux through any closed surface is proportional to which quantity enclosed by that surface?

According to Gauss's law, the electric flux through any closed surface is proportional to which quantity enclosed by that surface?

• A. Enclosed charge Q_enclosed.
• B. Electric field magnitude.
• C. Volume of the surface.
• D. Surface area of the Gaussian surface.

Answer: (A)

Gauss’s law says that the net electric flux through a closed surface is determined by the total charge enclosed by that surface. Mathematically, the flux is Phi = Q_enclosed / epsilon0, where epsilon0 is the vacuum permittivity. This means the shape or size of the surface doesn’t matter—the only thing that matters is how much charge lies inside. Field lines crossing the surface contribute to the flux, and for charges outside the surface their lines enter and exit in a way that cancels out, so they don’t affect the total flux. That’s why the enclosed charge is the quantity that the flux is proportional to. The other quantities listed—electric field magnitude, the volume, or the surface area—do not alone determine the net flux; the flux depends on the enclosed charge, regardless of the surface’s particular geometry. If you place a positive charge inside, you get outward flux; a negative charge gives inward flux; and if no net charge is enclosed, the total flux is zero.

Gauss’s law says that the net electric flux through a closed surface is determined by the total charge enclosed by that surface. Mathematically, the flux is Phi = Q_enclosed / epsilon0, where epsilon0 is the vacuum permittivity. This means the shape or size of the surface doesn’t matter—the only thing that matters is how much charge lies inside. Field lines crossing the surface contribute to the flux, and for charges outside the surface their lines enter and exit in a way that cancels out, so they don’t affect the total flux.

That’s why the enclosed charge is the quantity that the flux is proportional to. The other quantities listed—electric field magnitude, the volume, or the surface area—do not alone determine the net flux; the flux depends on the enclosed charge, regardless of the surface’s particular geometry. If you place a positive charge inside, you get outward flux; a negative charge gives inward flux; and if no net charge is enclosed, the total flux is zero.