Law
Gauss's law
The total electric flux through a closed surface equals the enclosed charge divided by ε₀: ∮ E · dA = q_enclosed / ε₀. Powerful tool for fields with high symmetry.
-- NCERT Class 12 Physics, Ch. 1, p. 30Gauss's Law
8 MCQs1 revision card9-step worked example
Source: NCERT ElectrostaticsPYQ coverage: NEET 2023Official key: NTA-verifiedLast updated: 21 Sep 2026
Gauss's Law, explained for NEET
The trap: mixing up the two sides of Gauss's law. The field on the surface is produced by all charges, inside and outside. The charge on the right-hand side is only the charge enclosed. An outside charge changes E on the surface but adds nothing to the net flux.
The law. NCERT Class 12 Physics Part I, Chapter 1, Section 1.13 (page 30) states it without proof:
Electric flux through a closed surface S = q/ε₀ (Eq. 1.31, page 30)
where q is the total charge enclosed by S. For a point charge q at the centre of a sphere, adding E·ΔS over the sphere gives exactly q/ε₀ (Eq. 1.30, page 30), whatever the radius. The unit of flux is N m² C⁻¹.
Points NCERT lists (pages 30–31):
- The law holds for any closed surface, whatever its shape or size.
- q is the algebraic sum of all charges inside, wherever they sit inside.
- The field in the flux is due to charges inside and outside; q counts only the inside.
- The chosen surface is the Gaussian surface. It must not pass through a discrete charge, because the field is not well defined there. It may pass through a continuous charge distribution.
- The law rests on the inverse square dependence in Coulomb's law.
Zero flux. If no charge is enclosed, the net flux is zero. NCERT's check (page 30): a closed cylinder with its axis along a uniform field has −ES through one flat face, +ES through the other and zero through the curved side. Conversely, zero net flux tells you the total enclosed charge is zero — not that there is no charge, and not that E is zero on the surface.
Bridge to NEET. Questions list charges inside and outside a surface and ask for the flux, or give the flux and ask for the enclosed charge (q = ε₀φ). Distractors: counting outside charges, adding magnitudes instead of signed charges, multiplying by ε₀ instead of dividing.
Watch out: positive net outward flux means net positive enclosed charge; negative flux means net negative charge.
Can you answer these Gauss's Law MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
According to Gauss's law as stated in NCERT, the net electric flux through a closed surface equals:
Show answer and why every option is right or wrong
Answer: A. NCERT Class 12 Physics Part I, Chapter 1, Eq. 1.31 (page 30): flux through a closed surface S = q/ε₀, with q the total charge enclosed by S.
Why B is wrong: B is wrong because it multiplies the charge by ε₀; the law divides by ε₀ (it is the enclosed charge that equals ε₀ times the flux).
Why C is wrong: C is wrong because charges outside the surface are not counted in q; NCERT says q represents only the total charge inside S.
Why D is wrong: D is wrong because q/4πε₀r² is the form of a point-charge field magnitude, not a flux; the flux q/ε₀ does not depend on the size of the surface.
MCQ 2Easy RecallPractice
A closed surface is drawn so that some charges lie inside it and some lie outside it. Which statement about the charges outside is correct?
Show answer and why every option is right or wrong
Answer: C. NCERT Class 12 Physics Part I, Chapter 1, page 30, point (iii): the field whose flux appears on the left of Eq. 1.31 is due to all charges, inside and outside, while q on the right is only the charge inside S.
Why A is wrong: A is wrong because it counts outside charges in the net flux; the net flux equals only the enclosed charge divided by ε₀.
Why B is wrong: B is wrong because outside charges do produce a field at points on the surface; their contributions to the flux simply add up to zero over the closed surface.
Why D is wrong: D is wrong because it reverses the roles: outside charges change the field on the surface but leave the net flux unchanged.
MCQ 3Easy RecallPractice
For which surfaces does Gauss's law, flux = q/ε₀, hold?
Show answer and why every option is right or wrong
Answer: B. NCERT Class 12 Physics Part I, Chapter 1, page 30, point (i): Gauss's law is true for any closed surface, no matter what its shape or size.
Why A is wrong: A is wrong because the sphere with a central charge is only NCERT's simple illustration (Eq. 1.30); the general result holds for any closed surface.
Why C is wrong: C is wrong because symmetry only makes the law useful for finding E easily (NCERT's point on symmetry, p.31); the law itself holds for every closed surface.
Why D is wrong: D is wrong because the law is about the net flux through a closed surface; an open surface does not enclose any charge.
MCQ 4Direct ApplicationPYQ Pattern
Point charges +3.0 µC, −5.0 µC and +4.0 µC lie inside a closed surface. A charge of +6.0 µC lies outside it. What is the net outward electric flux through the surface? (ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻²)
Show answer and why every option is right or wrong
Answer: C. Enclosed charge q = 3.0 − 5.0 + 4.0 = +2.0 µC = 2.0 × 10⁻⁶ C. Flux = q/ε₀ = 2.0 × 10⁻⁶ / 8.854 × 10⁻¹² ≈ 2.3 × 10⁵ N m² C⁻¹ (NCERT Chapter 1, Eq. 1.31, page 30).
Why A is wrong: A is wrong because 9.0 × 10⁵ comes from adding the outside +6.0 µC to the enclosed charge (8.0 µC / ε₀); outside charges do not count in q.
Why B is wrong: B is wrong because 1.4 × 10⁶ comes from adding magnitudes, 3.0 + 5.0 + 4.0 = 12 µC; q is the algebraic sum, so the −5.0 µC must be subtracted.
Why D is wrong: D is wrong because 1.8 × 10⁻¹⁷ comes from multiplying 2.0 × 10⁻⁶ C by ε₀ instead of dividing by it.
MCQ 5Direct ApplicationPYQ Pattern
The net outward electric flux through a closed surface is found to be 4.5 × 10³ N m² C⁻¹. What is the net charge enclosed? (ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻²)
Show answer and why every option is right or wrong
Answer: B. q = ε₀φ = 8.854 × 10⁻¹² × 4.5 × 10³ ≈ 4.0 × 10⁻⁸ C. The flux is outward (positive), so the net enclosed charge is positive (NCERT Chapter 1, Eq. 1.31, page 30; Example 1.11 uses q = ε₀φ).
Why A is wrong: A is wrong because 5.1 × 10¹⁴ comes from dividing the flux by ε₀ (4.5 × 10³ / 8.854 × 10⁻¹²); the charge is ε₀ times the flux, not the flux divided by ε₀.
Why C is wrong: C is wrong because 5.0 × 10⁻⁷ comes from multiplying the flux by 4πε₀ (4.5 × 10³ × 1.113 × 10⁻¹⁰); Gauss's law has ε₀ alone, with no 4π.
Why D is wrong: D is wrong because it flips the sign; a positive net outward flux means the net enclosed charge is positive.
MCQ 6Direct ApplicationPYQ Pattern
A point charge of +1.77 nC is placed at the centre of a closed cubical surface of side 0.20 m. What is the net outward electric flux through the whole cube? (ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻²)
Show answer and why every option is right or wrong
Answer: D. Gauss's law holds for any closed surface, so the cube's shape and size do not matter: flux = q/ε₀ = 1.77 × 10⁻⁹ / 8.854 × 10⁻¹² ≈ 2.0 × 10² N m² C⁻¹ (NCERT Chapter 1, Eq. 1.31 and point (i), page 30).
Why A is wrong: A is wrong because 33 is q/6ε₀, the flux through only one of the six faces; the question asks for the whole closed cube.
Why B is wrong: B is wrong because 5.0 × 10³ comes from dividing q/ε₀ by the side squared (0.040 m²); the flux through a closed surface does not depend on its size.
Why C is wrong: C is wrong because 1.6 × 10³ is the field magnitude q/4πε₀r² at r = 0.10 m (the centre of a face), a field in N/C, not the flux through the cube.
MCQ 7CalculationPYQ Pattern
Closed surface S₁ encloses only a charge q₁ = +2.0 nC. A larger closed surface S₂ encloses both q₁ and a second charge q₂ = −5.0 nC. What is the ratio φ₂/φ₁ of the net outward fluxes through S₂ and S₁?
Show answer and why every option is right or wrong
Answer: D. φ₁ = (+2.0 nC)/ε₀ and φ₂ = (2.0 − 5.0) nC/ε₀ = (−3.0 nC)/ε₀. So φ₂/φ₁ = −3.0/2.0 = −1.5; the larger surface has more inward than outward flux (NCERT Chapter 1, page 30, point (ii)).
Why A is wrong: A is wrong because −2.5 = q₂/q₁ uses only q₂ for S₂; S₂ also encloses q₁, so its enclosed charge is −3.0 nC.
Why B is wrong: B is wrong because 3.5 = (2.0 + 5.0)/2.0 adds the magnitudes; the enclosed charge is the algebraic sum, 2.0 − 5.0 = −3.0 nC.
Why C is wrong: C is wrong because +1.5 drops the sign; S₂ has net negative enclosed charge, so its net outward flux is negative.
MCQ 8Concept TrapPractice
The net outward electric flux through a closed surface is zero. Which conclusion is correct?
Show answer and why every option is right or wrong
Answer: A. NCERT Class 12 Physics Part I, Chapter 1, page 30: whenever the net flux through a closed surface is zero, the total charge contained is zero. The field on the surface can still be non-zero, as in NCERT's closed cylinder in a uniform field, where the flat faces carry −ES and +ES.
Why B is wrong: B is wrong because zero net flux does not mean zero field; in NCERT's cylinder example the field is non-zero on both flat faces while the total flux is zero.
Why C is wrong: C is wrong because charges outside the surface can be present; they produce a field on the surface but add nothing to the net flux.
Why D is wrong: D is wrong because Gauss's law fixes only the algebraic sum; +q and −q inside together give zero enclosed charge and zero net flux.
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Gauss's Law: quick recall before you leave
How do you solve a Gauss's Law question? A worked example
- 1
Given
• Field: E = +200 î N/C for x > 0 and E = −200 î N/C for x < 0. The magnitude is taken as 2.00 × 10² N/C (three significant figures, matching NCERT's three-figure answers).• A right circular cylinder of length 20 cm (0.200 m) and radius 5 cm (0.0500 m), centre at the origin, axis along the x-axis; its flat faces are at x = +10 cm and x = −10 cm.• ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻².
- 2
Required
(a) Net outward flux through each flat face. (b) Flux through the curved side. (c) Net outward flux through the cylinder. (d) Net charge inside the cylinder.
- 3
Concept
Flux through a small area is E·ΔS, with ΔS along the outward normal. On each flat face E is uniform and parallel to the normal line; on the curved side E is perpendicular to the normal. Once the total flux through the closed cylinder is known, Gauss's law gives the enclosed charge.
- 4
Formula
Flux through a face = E·ΔS; net flux φ = sum over all faces; Gauss's law φ = q/ε₀, so q = ε₀φ (NCERT Chapter 1, Eq. 1.31, page 30).
- 5
Substitution
• Face area ΔS = π(0.05)² m².• Left face (x = −10 cm): E = −200 î N/C, outward normal along −î, so E·ΔS = +200 ΔS = +200 × π(0.05)².• Right face (x = +10 cm): E = +200 î N/C, outward normal along +î, so E·ΔS = +200 × π(0.05)².• Curved side: E ⟂ ΔS, so E·ΔS = 0.• q = 8.854 × 10⁻¹² × φ.
- 6
Calculation
• (a) Each flat face: 200 × π × 0.0025 = +1.57 N m² C⁻¹.• (b) Curved side: 0.• (c) φ = 1.57 + 1.57 + 0 = 3.14 N m² C⁻¹.• (d) q = 3.14 × 8.854 × 10⁻¹² C = 2.78 × 10⁻¹¹ C.
π and the counting number 2 (two flat faces) are exact and do not limit the significant figures; the answers carry three significant figures, as in NCERT. - 7
Final answer
Each flat face: +1.57 N m² C⁻¹; curved side: 0; net outward flux: 3.14 N m² C⁻¹; net enclosed charge: 2.78 × 10⁻¹¹ C.
- 8
Common trap
Giving the left face a negative flux because the field there points along −x. The sign comes from the angle between E and the outward normal: on the left face both point along −x, so that flux is positive too. Taking it as −1.57 would give a net flux of zero and the wrong conclusion that the cylinder holds no charge.
- 9
Similar NEET-style question
"The field is E = +3.00 × 10² î N/C for x > 0 and E = −3.00 × 10² î N/C for x < 0. A closed right circular cylinder of radius 0.100 m and length 0.400 m has its centre at the origin and its axis along the x-axis. Find the net charge inside the cylinder."
Strategy: Each flat face gives +300 × π(0.100)² = +9.42 N m² C⁻¹ and the curved side gives zero, so φ = 18.8 N m² C⁻¹ and q = ε₀φ ≈ 1.67 × 10⁻¹⁰ C. The length does not enter the answer.
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What to remember before solving Gauss's Law questions
Which Gauss's Law formulas do you need for NEET?
1 formula — click to collapse
Gauss's law
Total electric flux through closed surface equals enclosed charge over permittivity.
| Symbol | Quantity | SI Unit |
|---|---|---|
| Phi_E | total flux | V*m |
| Q_enc | enclosed charge | C |
Valid when
- Closed surface
- All sources accounted for
More in Electrostatics: 3 exam traps and mistakes · 10 formulas · 5 question patterns from its other lessons.
Gauss's Law questions from past NEET papers
1 question from NEET 2023. Answers verified against NTA official keys. — click to collapse
NEET 2023
If ∮ₛ E⃗ · dS⃗ = 0 over a surface, then
1The magnitude of electric field on the surface is constant
2All the charges must necessarily be inside the surface
3The electric field inside the surface is necessarily uniform
4The number of flux lines entering the surface must be equal to the number of flux lines leaving it
NTA Answer: Option 4(final)
How does NEET ask about Gauss's Law?
1 recurring pattern from past papers — click to collapse
Charged spherical shell: field inside zero, outside as point charge. Apply Gauss's law to find E at given r.
InterpretationMedium
Common distractors
treats shell like solid sphere
Includes interior charge contribution where there is none
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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