Match the surface in List-I with the total electric flux through it in List-II.
| List-I | List-II |
|---|---|
| (A) A closed surface that encloses the charges \(+3q\) and \(-q\) | (I) \(q/\varepsilon_0\) |
| (B) One face of a cube that has a charge \(q\) at its centre | (II) Zero |
| (C) A closed surface with a charge \(q\) placed just outside it | (III) \(2q/\varepsilon_0\) |
| (D) A sphere that encloses a charge \(q\), with another charge \(q\) placed outside it | (IV) \(q/6\varepsilon_0\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
By Gauss’s law, the total flux through a closed surface is \( q/\varepsilon_0 \), where \( q \) is the total charge inside the surface. Charges outside the surface add nothing to this total.
(A) A closed surface that encloses the charges \( +3q \) and \( -q \) — This matches (III) \( 2q/\varepsilon_0 \). The charge inside is \( 3q-q=2q \).
(B) One face of a cube that has a charge \( q \) at its centre — This matches (IV) \( q/6\varepsilon_0 \). The whole cube is a closed surface with flux \( q/\varepsilon_0 \). Its six faces are alike as seen from the centre, so each face gets one-sixth of it.
(C) A closed surface with a charge \( q \) placed just outside it — This matches (II) zero. The surface encloses no charge. Every field line of \( q \) that enters the surface also leaves it.
(D) A sphere that encloses a charge \( q \), with another charge \( q \) placed outside it — This matches (I) \( q/\varepsilon_0 \). The outside charge changes the field on the sphere, but only the charge inside fixes the total flux.
NCERT (2026-27):
Gauss’s Law – “(ii) The term q on the right side of Gauss’s law … includes the sum of all charges enclosed by the surface.”
Gauss’s Law – “(i) Gauss’s law is true for any closed surface, no matter what its shape or size.”
Gauss’s Law – “The law implies that the total electric flux through a closed surface is zero if no charge is enclosed by the surface.”
Gauss’s Law – “(iii) In the situation when the surface is so chosen that there are some charges inside and some outside, the electric field … is due to all the charges, both inside and outside S. The term q on the right side of Gauss’s law, however, represents only the total charge inside S.”