E = σ / (2ε₀), where σ is surface charge density. Independent of distance from sheet (uniform field).
-- NCERT Class 12 Physics, Ch. 1, p. 35Field Plane Sheet Gauss
8 MCQs1 revision card9-step worked example
Source: NCERT ElectrostaticsOfficial key: NTA-verifiedLast updated: 21 Sep 2026
Field Plane Sheet Gauss, explained for NEET
The trap: treating a charged plane sheet like a point charge and making its field fall off with distance. For a uniformly charged infinite plane sheet, NCERT Class 12 Physics Part I, Chapter 1 (page 35) notes that Gauss's law brings out an additional fact: E is independent of the distance x from the sheet. A second slip is dropping the factor 2 and writing σ/ε₀.
Where the 2 comes from (NCERT Section 1.14.2, page 34). Take the x-axis normal to the sheet. By symmetry, E is along x. Choose a Gaussian surface (a rectangular box or a cylinder) that pierces the sheet, with two flat faces of area A, one on each side. Field lines are parallel to the other faces, so only the two flat faces carry flux, and the two fluxes add: net flux = 2EA. The charge enclosed is σA. Gauss's law gives 2EA = σA/ε₀, so
E = σ / 2ε₀ (NCERT Chapter 1, Eq. 1.33, page 35)
σ is the surface charge density (C m⁻²); E comes out in N C⁻¹.
Direction (page 35). E is normal to the sheet. It points away from the sheet if σ is positive and toward the sheet if σ is negative, on both sides.
Real sheets. For a finite but large sheet, Eq. 1.33 is approximately true in the middle regions, away from the ends (page 35).
Bridge to NEET. Questions in this area give σ and ask for E, give E and ask for σ, or change the distance and ask what happens to E. Distractors come from forgetting the 2, inverting the ratio, borrowing 4πε₀ from the point-charge formula, or scaling E by 1/x or 1/x².
Watch out: if the stem gives a distance from an infinite sheet, the distance does not enter the field calculation. Check that it is not a finite sheet viewed from far away before ignoring it.
Can you answer these Field Plane Sheet Gauss 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
An infinite plane sheet carries a uniform surface charge density σ. The magnitude of the electric field at a point near it is:
Show answer and why every option is right or wrong
Answer: C. Gauss's law with a surface crossing the sheet gives 2EA = σA/ε₀, so E = σ/(2ε₀) (NCERT Class 12 Physics Part I, Chapter 1, Eq. 1.33, page 35).
Why A is wrong: A is wrong because σ/ε₀ counts the flux through only one flat face (EA = σA/ε₀); the Gaussian surface has two flat faces, one on each side, so the net flux is 2EA.
Why B is wrong: B is wrong because it makes the field fall with distance as if the sheet were a line or point source; for an infinite sheet E does not depend on x.
Why D is wrong: D is wrong because it multiplies by 2 instead of dividing; 2EA = σA/ε₀ puts the 2 in the denominator.
MCQ 2Easy RecallPractice
How does the magnitude of the electric field of a uniformly charged infinite plane sheet vary with the distance x from the sheet?
Show answer and why every option is right or wrong
Answer: D. NCERT Class 12 Physics Part I, Chapter 1, page 35: the Gauss's-law result E = σ/(2ε₀) shows that E is independent of x.
Why A is wrong: A is wrong because 1/x² is the point-charge dependence; the plane-sheet result σ/(2ε₀) contains no distance at all.
Why B is wrong: B is wrong because 1/x is the pattern for a long line of charge, not for a plane sheet; σ/(2ε₀) has no x in it.
Why C is wrong: C is wrong because nothing in σ/(2ε₀) grows with distance; the field neither increases nor decreases as you move away from an infinite sheet.
MCQ 3Easy RecallPractice
An infinite plane sheet has a uniform negative surface charge density. The electric field at points on either side of the sheet is:
Show answer and why every option is right or wrong
Answer: A. NCERT Class 12 Physics Part I, Chapter 1, page 35: E is normal to the sheet, directed away from it if σ is positive and toward it if σ is negative. With σ negative, E points toward the sheet on both sides.
Why B is wrong: B is wrong because away from the sheet is the direction for positive σ; for negative σ the field points toward the sheet.
Why C is wrong: C is wrong because by symmetry the field of an infinite plane sheet is normal to the sheet; that is why no flux passes through the Gaussian surface's side faces.
Why D is wrong: D is wrong because it treats the field as pointing the same way in space on both sides; for a sheet of one sign the field points toward the sheet from both sides.
MCQ 4Direct ApplicationPractice
An infinite plane sheet has a uniform surface charge density of 8.85 × 10⁻⁸ C m⁻². Taking ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻², the magnitude of the electric field near the sheet is:
Show answer and why every option is right or wrong
Answer: B. E = σ/(2ε₀) = (8.85 × 10⁻⁸)/(2 × 8.85 × 10⁻¹²) = 5.00 × 10³ N C⁻¹ (NCERT Class 12 Physics Part I, Chapter 1, Eq. 1.33, page 35).
Why A is wrong: A is wrong because 1.00 × 10⁴ comes from σ/ε₀ = (8.85 × 10⁻⁸)/(8.85 × 10⁻¹²), dropping the factor 2 in the denominator.
Why C is wrong: C is wrong because 7.96 × 10² comes from σ/(4πε₀) = 1.00 × 10⁴/(4π), borrowing the 4π of the point-charge formula instead of using 2.
Why D is wrong: D is wrong because 2.00 × 10⁻⁴ comes from 2ε₀/σ = (1.77 × 10⁻¹¹)/(8.85 × 10⁻⁸), inverting the ratio.
MCQ 5Direct ApplicationPractice
The electric field at a point 5.0 cm from a uniformly charged infinite plane sheet is 3.0 × 10⁴ N C⁻¹. Taking ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻², the surface charge density of the sheet is:
Show answer and why every option is right or wrong
Answer: C. From E = σ/(2ε₀), σ = 2ε₀E = 2 × 8.85 × 10⁻¹² × 3.0 × 10⁴ = 5.31 × 10⁻⁷ ≈ 5.3 × 10⁻⁷ C m⁻². The 5.0 cm is not needed, because E does not depend on distance (NCERT Class 12 Physics Part I, Chapter 1, Eq. 1.33, page 35).
Why A is wrong: A is wrong because 2.7 × 10⁻⁷ comes from σ = ε₀E = 8.85 × 10⁻¹² × 3.0 × 10⁴ = 2.655 × 10⁻⁷, dropping the factor 2.
Why B is wrong: B is wrong because 1.1 × 10⁻⁵ comes from dividing the correct 5.31 × 10⁻⁷ by the distance 0.050 m; the distance does not enter the plane-sheet formula.
Why D is wrong: D is wrong because 5.9 × 10⁻¹⁶ comes from 2ε₀/E = (1.77 × 10⁻¹¹)/(3.0 × 10⁴), dividing by E where the formula multiplies by E.
MCQ 6Direct ApplicationPractice
The electric field at 2.0 cm from a uniformly charged infinite plane sheet is 4.0 × 10³ N C⁻¹. What is the field at 8.0 cm from the same sheet, on the same side?
Show answer and why every option is right or wrong
Answer: A. E = σ/(2ε₀) does not depend on distance, so the field at 8.0 cm is the same, 4.0 × 10³ N C⁻¹ (NCERT Class 12 Physics Part I, Chapter 1, page 35).
Why B is wrong: B is wrong because 2.5 × 10² comes from scaling as 1/x²: 4.0 × 10³ × (2.0/8.0)², treating the sheet like a point charge.
Why C is wrong: C is wrong because 1.6 × 10⁴ comes from making E proportional to x: 4.0 × 10³ × (8.0/2.0); the field of an infinite sheet does not grow with distance.
Why D is wrong: D is wrong because 1.0 × 10³ comes from scaling as 1/x: 4.0 × 10³ × (2.0/8.0); that is the line-charge pattern, not the plane-sheet result.
MCQ 7CalculationPractice
An infinite plane sheet has uniform surface charge density 1.77 × 10⁻⁸ C m⁻². A closed Gaussian cylinder with its axis perpendicular to the sheet passes through it; each flat end face has area 5.0 × 10⁻² m², one face on each side. Taking ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻², the electric flux through ONE flat end face is:
Show answer and why every option is right or wrong
Answer: B. E = σ/(2ε₀) = (1.77 × 10⁻⁸)/(1.77 × 10⁻¹¹) = 1.00 × 10³ N C⁻¹, normal to the face, so flux through one face = EA = 1.00 × 10³ × 5.0 × 10⁻² = 5.0 × 10¹ N m² C⁻¹. The two faces together give 2EA = σA/ε₀ = 1.0 × 10² (NCERT Class 12 Physics Part I, Chapter 1, Section 1.14.2, pages 34–35).
Why A is wrong: A is wrong because 1.0 × 10² = σA/ε₀ is the net flux through the whole closed surface, which is shared equally by the two end faces.
Why C is wrong: C is wrong because zero is the flux through the curved side, where the field lines run parallel to the surface; at the end faces E is normal to the face.
Why D is wrong: D is wrong because 2.0 × 10⁴ comes from E/A = 1.00 × 10³/(5.0 × 10⁻²), dividing by the area where flux multiplies by it.
MCQ 8CalculationPractice
Point P is 1.0 cm from a uniformly charged infinite plane sheet. The surface charge density of the sheet is doubled, and the field is now measured at point Q, 4.0 cm from the sheet. The ratio E_Q (new) : E_P (original) is:
Show answer and why every option is right or wrong
Answer: D. E = σ/(2ε₀) is proportional to σ and independent of distance. Doubling σ doubles E; moving from 1.0 cm to 4.0 cm changes nothing. So E_Q : E_P = 2 : 1 (NCERT Class 12 Physics Part I, Chapter 1, Eq. 1.33 and the independence of x, page 35).
Why A is wrong: A is wrong because 1 : 8 comes from 2 × (1.0/4.0)² = 1/8, applying a point-charge 1/x² fall-off that a plane sheet does not have.
Why B is wrong: B is wrong because 1 : 2 comes from 2 × (1.0/4.0) = 1/2, applying a 1/x fall-off that belongs to a line charge, not a plane sheet.
Why C is wrong: C is wrong because 8 : 1 comes from 2 × (4.0/1.0) = 8, making the field grow with distance; the plane-sheet field does not depend on distance.
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Field Plane Sheet Gauss: quick recall before you leave
How do you solve a Field Plane Sheet Gauss question? A worked example
Pattern: no in-scope PYQ pattern in this dossier; original numeric problem.
- 1
Given
A large thin sheet, treated as an infinite plane sheet, carries a uniform surface charge density σ = +1.77 × 10⁻⁷ C m⁻². Point P is 2.0 cm from the sheet; point R is 6.0 cm from the sheet on the opposite side. Take ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻².
- 2
Required
(a) The magnitude of E at P. (b) The magnitude of E at R. (c) The direction of E at P and at R.
- 3
Concept
Gauss's law applied to a surface crossing the sheet gives a field that is normal to the sheet and independent of distance. For positive σ the field points away from the sheet on both sides.
- 4
Formula
E = σ / (2ε₀) (NCERT Class 12 Physics Part I, Chapter 1, Eq. 1.33, page 35)
- 5
Substitution
E = (1.77 × 10⁻⁷ C m⁻²) / (2 × 8.85 × 10⁻¹² C² N⁻¹ m⁻²)
- 6
Calculation
2 × 8.85 × 10⁻¹² = 1.77 × 10⁻¹¹
E = (1.77 × 10⁻⁷)/(1.77 × 10⁻¹¹) = 1.00 × 10⁴ N C⁻¹
The distances 2.0 cm and 6.0 cm do not enter the calculation. The factor 2 is an exact counting number from the two flat faces and does not limit significant figures; σ and ε₀ are given to three significant figures, so E is reported to three. - 7
Final answer
(a) E at P = 1.00 × 10⁴ N C⁻¹; (b) E at R = 1.00 × 10⁴ N C⁻¹; (c) at both points E is perpendicular to the sheet and points away from it (σ is positive).
- 8
Common trap
Scaling the field at R down from P as if the sheet were a point charge: 1.00 × 10⁴ × (2.0/6.0)² ≈ 1.1 × 10³ N C⁻¹. That is wrong; the plane-sheet field is the same at both points. Also check the 2: using σ/ε₀ would give 2.00 × 10⁴ N C⁻¹, double the correct value.
- 9
Similar NEET-style question
"An infinite plane sheet carries a uniform surface charge density of −3.54 × 10⁻⁸ C m⁻². Find the magnitude and direction of the electric field at a point 10 cm from the sheet. (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²)"
Strategy: E = |σ|/(2ε₀) = (3.54 × 10⁻⁸)/(1.77 × 10⁻¹¹) = 2.00 × 10³ N C⁻¹, perpendicular to the sheet and directed toward it because σ is negative. The 10 cm is not used.
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What to remember before solving Field Plane Sheet Gauss questions
Which Field Plane Sheet Gauss formulas do you need for NEET?
1 formula — click to collapse
Field of charged plane sheet
Uniform field perpendicular to a non-conducting infinite plane sheet of surface charge density sigma. Independent of distance.
| Symbol | Quantity | SI Unit |
|---|---|---|
| sigma | surface charge density | C/m^2 |
| eps0 | permittivity | F/m |
Valid when
- Infinite plane sheet
- Non-conducting (otherwise sigma is split between surfaces)
More in Electrostatics: 3 exam traps and mistakes · 10 formulas · 6 question patterns from its other lessons.
Field Plane Sheet Gauss questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
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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