If the flux of the electric field through a closed surface is zero.
(A) The electric field must be zero everywhere on the surface.
(B) The electric field may be zero everywhere on the surface.
(C) The charge inside the surface must be zero.
(D) The charge in the vicinity of its surface must be zero.
(E) The charge inside the surface may be zero.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B), (C) only
By Gauss’s law the flux through a closed surface is \( \Phi = \frac{q_{\mathrm{enc}}}{\varepsilon_0} \), where \( q_{\mathrm{enc}} \) is the net charge inside. Zero flux means zero net charge inside, but it does not mean zero field on the surface: the field there is due to all charges, inside and outside, and the flux in equals the flux out.
(A) The electric field must be zero everywhere on the surface — Incorrect. The flux can be zero with a non-zero field, for example a neutral surface in the field of a charge placed outside it.
(B) The electric field may be zero everywhere on the surface — Correct. This is possible, for example when there is no charge anywhere near the surface.
(C) The charge inside the surface must be zero — Correct. Taken as the net charge inside, \( q_{\mathrm{enc}} = \varepsilon_0\Phi = 0 \).
(D) The charge in the vicinity of its surface must be zero — Incorrect. Charges just outside the surface contribute flux in and out that cancel, so they need not vanish.
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. … (iii) In the situation when the surface is so chosen that there are some charges inside and some outside, the electric field [whose flux appears on the left side of Eq. (1.31)] is due to all the charges, both inside and outside S.”