Gauss's law \( \phi_E = \displaystyle\frac{q}{\varepsilon_0} \) is TRUE for
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → any closed surface, no matter what its shape and size
Gauss’s law states that the total electric flux through a closed surface equals the net charge enclosed divided by \( \varepsilon_0 \). Every field line from the enclosed charge crosses the surface, whatever its shape or size; for a sphere, E falls as \( 1/r^{2} \) while the area grows as \( r^{2} \).
\( \displaystyle \phi_E = E \times 4\pi r^{2} = \frac{q}{4\pi\varepsilon_0 r^{2}} \times 4\pi r^{2} = \frac{q}{\varepsilon_0} \)
Option (1) any closed surface, no matter what its shape and size — Correct. The flux depends only on the charge enclosed.
Option (2) any closed surface, independent of shape but depends on size of the surface. — Incorrect. The flux does not depend on the size.
Option (3) any surface, no matter what its shape or size. — Incorrect. Some field lines miss an open surface; the law holds only for a closed surface.
Option (4) any closed surface, but depends on its shape and size. — Incorrect. The flux is independent of both shape and size.
NCERT (2026-27):
Gauss’s Law – “… The great significance of Gauss’s law Eq. (1.31), is that it is true in general, and not only for the simple cases we have considered above. Let us note some important points regarding this law:
(i) Gauss’s law is true for any closed surface, no matter what its shape or size.”