Select the correct statement from the following
A. Gauss's law is true for any closed surface, no matter what its shape or size.
B. If the net electric flux through a closed surface is zero, we can conclude that the total charge contained in the closed surface is also zero.
C. Gauss's law is not based on the inverse square dependence on distance contained in the coulomb's law.
D. The electric field due to a charge outside the Gaussian surface contributes zero net flux through the surface.
Choose the correct answer from the options given below
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, B and D only
Gauss's law states that the total electric flux through any closed surface equals the net charge enclosed divided by \( \varepsilon_0 \).
\( \displaystyle \oint \vec{E}\cdot d\vec{S} = \frac{q_{\mathrm{enc}}}{\varepsilon_0} \)
A. Gauss's law is true for any closed surface, no matter what its shape or size. — Correct. The law holds for every closed surface; the shape is chosen only to make the calculation easy.
B. If the net electric flux through a closed surface is zero, we can conclude that the total charge contained in the closed surface is also zero. — Correct. Zero flux gives \( q_{\mathrm{enc}} = 0 \); the total (algebraic sum of the) charge enclosed is zero.
C. Gauss's law is not based on the inverse square dependence on distance contained in the coulomb's law. — Incorrect. Gauss's law rests on the inverse square law: the field of a point charge falls as \( 1/r^{2} \) while the area of a sphere grows as \( r^{2} \), so the flux is the same through every sphere around the charge. Any other power of \( r \) would break the law.
D. The electric field due to a charge outside the Gaussian surface contributes zero net flux through the surface. — Correct. Every field line from an outside charge that enters the surface also leaves it, so its net flux is zero.
NCERT (2026-27):
Gauss’s Law – “… Thus, whenever you find that the net electric flux through a closed surface is zero, we conclude that the total charge contained in the closed surface is zero. … (i) Gauss’s law is true for any closed surface, no matter what its shape or size.”
Gauss’s Law – “… (vi) Finally, Gauss’s law is based on the inverse square dependence on distance contained in the Coulomb’s law.”