Definition
Electric flux
Φ_E = ∫ E · dA. Quantifies number of field lines crossing a surface. SI unit: V·m or N·m²/C.
-- NCERT Class 12 Physics, Ch. 1, p. 22Electric Flux
8 MCQs9-step worked example
Source: NCERT ElectrostaticsOfficial key: NTA-verifiedLast updated: 21 Sep 2026
Electric Flux, explained for NEET
The trap: putting the wrong angle into cos θ. In the flux formula, θ is the angle between the field E and the area vector ΔS, and the area vector points along the normal to the surface. If a question gives the angle between E and the plane of the surface, the angle you need is 90° minus that.
The definition. NCERT Class 12 Physics Part I, Chapter 1, Section 1.9 (page 22) defines the electric flux through a small area element as
Δφ = E · ΔS = E ΔS cos θ (Eq. 1.11, page 22)
It is proportional to the number of field lines cutting the area element. NCERT's footnote on page 22 warns that it is not proper to say the flux equals the number of lines, because how many lines you draw is a choice.
Reading cos θ.
- θ = 0°: the normal is along E; the flux is E ΔS, its largest value.
- θ = 90°: the field lines run parallel to the surface and do not cross it; the flux is zero (page 22).
- θ = 180°: the normal points against E; the flux is −E ΔS.
Which way does the normal point? A normal can point two ways. For a closed surface, NCERT's convention is the outward normal (page 22). So on a face where the field enters the closed surface, the flux is negative.
Unit and total. The unit of electric flux is N C⁻¹ m² (page 23). For a larger surface, divide it into small elements and add: φ ≈ Σ E · ΔS (Eq. 1.12, page 23). The sum becomes exact as ΔS → 0, when it is written as an integral.
Bridge to NEET. Flux questions usually give E, an area and an angle, or a field written in components. Take the dot product with the normal. Do not multiply the magnitude of E by the area when E is tilted.
Watch out: on the faces of a closed box that are parallel to E, the flux is zero. It is not E × area.
Can you answer these Electric Flux 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
What is the unit of electric flux given in NCERT?
Show answer and why every option is right or wrong
Answer: A. Flux is E · ΔS, so its unit is (N C⁻¹) × m² = N C⁻¹ m². NCERT Class 12 Physics Part I, Chapter 1, page 23.
Why B is wrong: B is wrong because N m² C⁻² is the unit of the Coulomb constant 1/4πε₀, not of flux; flux has C⁻¹ to the first power.
Why C is wrong: C is wrong because N C⁻¹ is the unit of the electric field E alone; it leaves out the area that flux is multiplied by.
Why D is wrong: D is wrong because it divides the field unit by area (m⁻²); flux multiplies E by area, so the metre power is +2.
MCQ 2Easy RecallPractice
When flux is calculated through a closed surface, in which direction does NCERT take the area vector of each small element?
Show answer and why every option is right or wrong
Answer: B. NCERT Class 12 Physics Part I, Chapter 1, page 22: for a closed surface, the vector for every area element is taken along the outward normal, so ΔS = ΔS n̂ with n̂ the outward unit normal.
Why A is wrong: A is wrong because the convention is the outward normal; using the inward normal flips the sign of every flux value.
Why C is wrong: C is wrong because the area vector depends only on how the surface is oriented, not on the field; θ is the angle between E and this normal, and it is not always zero.
Why D is wrong: D is wrong because the direction of a planar area is along its normal; a tangent lies in the surface, and E along a tangent gives zero flux.
MCQ 3Easy RecallPractice
Which statement about the electric flux through a small area element is correct according to NCERT?
Show answer and why every option is right or wrong
Answer: D. NCERT Class 12 Physics Part I, Chapter 1, page 22: Δφ = E ΔS cos θ is proportional to the number of field lines cutting the element. The footnote says it is not proper to call it equal, since the number of lines drawn is a choice.
Why A is wrong: A is wrong because NCERT's footnote on page 22 says the number of field lines is not equal to E ΔS; only the relative number of lines is physically meaningful.
Why B is wrong: B is wrong because field lines parallel to the element do not cross it, which is θ = 90° and zero flux; the flux is largest when the normal is along E.
Why C is wrong: C is wrong because the flux contains cos θ; tilting the element reduces the number of lines crossing it, so its orientation matters.
MCQ 4Direct ApplicationPractice
A flat surface of area 5.0 × 10⁻² m² is placed in a uniform electric field of magnitude 2.0 × 10³ N C⁻¹. The normal to the surface makes an angle of 60° with the field. What is the electric flux through the surface?
Show answer and why every option is right or wrong
Answer: C. φ = E ΔS cos θ = (2.0 × 10³)(5.0 × 10⁻²)(cos 60°) = 1.0 × 10² × 0.5 = 5.0 × 10¹ N C⁻¹ m² (Eq. 1.11, NCERT Chapter 1, page 22).
Why A is wrong: A is wrong because 1.0 × 10² is E × ΔS with the cos 60° factor left out; that is the flux only when the normal is along E.
Why B is wrong: B is wrong because 8.7 × 10¹ = 1.0 × 10² × sin 60° uses sine instead of cosine; θ is measured from the normal, so cos θ applies.
Why D is wrong: D is wrong because 4.0 × 10⁴ comes from dividing E by the area (2.0 × 10³ / 5.0 × 10⁻²); flux multiplies E by the area.
MCQ 5Direct ApplicationPractice
A flat surface of area 2.0 × 10⁻¹ m² lies in a uniform electric field of magnitude 4.0 × 10² N C⁻¹. The plane of the surface makes an angle of 30° with the field. What is the electric flux through the surface?
Show answer and why every option is right or wrong
Answer: D. If the plane makes 30° with E, the normal makes 90° − 30° = 60° with E. So φ = (4.0 × 10²)(2.0 × 10⁻¹)(cos 60°) = 8.0 × 10¹ × 0.5 = 4.0 × 10¹ N C⁻¹ m² (Eq. 1.11, NCERT Chapter 1, page 22).
Why A is wrong: A is wrong because 6.9 × 10¹ = 8.0 × 10¹ × cos 30° puts the angle with the plane straight into cos θ; θ must be measured from the normal, which is 60° here.
Why B is wrong: B is wrong because 8.0 × 10¹ is E × ΔS with no cosine factor; the surface is tilted, so only part of the area faces the field.
Why C is wrong: C is wrong because 1.6 × 10² = 8.0 × 10¹ / cos 60° divides by the cosine instead of multiplying by it.
MCQ 6Direct ApplicationPractice
A uniform electric field of magnitude 3.0 × 10² N C⁻¹ points along +x. One face of a closed cube has area 4.0 × 10⁻² m², and its outward normal points along −x. What is the flux through this face?
Show answer and why every option is right or wrong
Answer: B. With the outward-normal convention (NCERT Chapter 1, page 22), θ = 180° between E and ΔS, so φ = E ΔS cos 180° = −(3.0 × 10²)(4.0 × 10⁻²) = −1.2 × 10¹ N C⁻¹ m². The field enters the cube through this face.
Why A is wrong: A is wrong because it takes θ = 0°, as if the area vector pointed along E; for a closed surface the outward normal is used, and here it points opposite to E.
Why C is wrong: C is wrong because zero flux needs θ = 90°, with field lines parallel to the face; this face is perpendicular to E, so the lines cross it.
Why D is wrong: D is wrong because 7.5 × 10³ comes from dividing E by the area (3.0 × 10² / 4.0 × 10⁻²); flux multiplies E by the area.
MCQ 7CalculationPractice
A flat surface in a uniform electric field has a flux of 6.0 N C⁻¹ m² through it when its normal is parallel to the field. The surface is then turned so that its normal makes 60° with the field, and the field strength is doubled. What is the new flux?
Show answer and why every option is right or wrong
Answer: C. At the start, E ΔS = 6.0 N C⁻¹ m². New flux = (2E) ΔS cos 60° = 2 × 6.0 × 0.5 = 6.0 N C⁻¹ m². Doubling E and halving cos θ cancel (Eq. 1.11, NCERT Chapter 1, page 22).
Why A is wrong: A is wrong because 3.0 = 6.0 × cos 60° includes the rotation but forgets that the field was doubled.
Why B is wrong: B is wrong because 1.2 × 10¹ = 2 × 6.0 includes the doubled field but leaves out the cos 60° factor from turning the surface.
Why D is wrong: D is wrong because 1.0 × 10¹ ≈ 2 × 6.0 × cos 30° uses the angle between the field and the plane (30°) instead of the angle with the normal (60°).
MCQ 8CalculationPractice
A uniform electric field is E = (3.0 î + 4.0 ĵ) N C⁻¹. A flat surface of area 0.50 m² lies in the y–z plane, with its area vector along +x. What is the electric flux through the surface?
Show answer and why every option is right or wrong
Answer: A. ΔS = 0.50 î m², so φ = E · ΔS = (3.0)(0.50) + (4.0)(0) = 1.5 N C⁻¹ m². Only the component of E along the normal contributes (NCERT Chapter 1, pages 22–23).
Why B is wrong: B is wrong because 2.0 = 4.0 × 0.50 uses the y-component; the y-component lies in the plane of the surface and gives no flux.
Why C is wrong: C is wrong because 3.5 = (3.0 + 4.0) × 0.50 adds the components as numbers; a dot product keeps only the component along the area vector.
Why D is wrong: D is wrong because 2.5 = |E| × ΔS = 5.0 × 0.50 uses the full magnitude of E; the field is not along the normal, so only its x-component counts.
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How do you solve a Electric Flux question? A worked example
- 1
Given
NCERT Class 12 Physics Part I, Chapter 1, Example 1.10 (page 31), Fig. 1.24. The electric field is E_x = αx^(1/2), E_y = E_z = 0, with α = 800 N C⁻¹ m^(−1/2) (NCERT writes "800 N/C m^1/2"). A cube of side a = 0.1 m has its left face at x = a and its right face at x = 2a. Both faces are perpendicular to the x-axis.
- 2
Required
(a) The net flux through the cube. (b) The charge inside the cube, as NCERT asks.
- 3
Concept
Flux through each face is E · ΔS, with the area vector along the outward normal. E has only an x-component, so on the four faces parallel to the x-axis the angle between E and ΔS is 90°, and their flux is zero. Only the left and right faces contribute. The field is not uniform, so E has a different value on each of those faces.
- 4
Formula
Δφ = E ΔS cos θ (Eq. 1.11, page 22).• Left face: θ = 180°, so φ_L = −E_L a².• Right face: θ = 0°, so φ_R = +E_R a².
For part (b), NCERT then uses q = φ ε₀, which is Gauss's law (Eq. 1.31, page 30). - 5
Substitution
E_L = α a^(1/2) (at x = a) and E_R = α (2a)^(1/2) (at x = 2a)
φ = φ_R + φ_L = a²(E_R − E_L) = α a² [(2a)^(1/2) − a^(1/2)] = α a^(5/2) (√2 − 1)
φ = 800 × (0.1)^(5/2) × (√2 − 1) - 6
Calculation
• (0.1)^(5/2) = 3.162 × 10⁻³• α a^(5/2) = 800 × 3.162 × 10⁻³ = 2.530• √2 − 1 = 0.4142• φ = 2.530 × 0.4142 = 1.048 ≈ 1.05 N m² C⁻¹• q = φ ε₀ = 1.05 × 8.854 × 10⁻¹² C, which NCERT prints as 9.27 × 10⁻¹² C. Multiplying directly gives 9.30 × 10⁻¹² C (or 9.28 × 10⁻¹² C with the unrounded flux 1.048), so NCERT's last digit doesn't follow from either; the lesson keeps NCERT's printed value. Any answer of 9.3 × 10⁻¹² C is the same result.
The numbers 2 and 5/2 in the exponents, √2 and the 1 in (√2 − 1) are exact mathematical constants. They do not limit the number of significant figures. NCERT gives the answers to three significant figures. - 7
Final answer
(a) Net flux through the cube = 1.05 N m² C⁻¹. (b) Charge inside = 9.27 × 10⁻¹² C (NCERT Example 1.10, page 32).
- 8
Common trap
Counting the left-face flux as positive. With the outward normal, θ = 180° on the left face, so its flux is −E_L a². If you add both magnitudes, you get α a^(5/2)(√2 + 1) = 2.530 × 2.414 ≈ 6.11 N m² C⁻¹. That is wrong. A second slip is giving the four faces parallel to the x-axis a non-zero flux, even though E is parallel to those faces.
- 9
Similar NEET-style question
"The electric field in a region is E = βx î, with β = 2.0 × 10² N C⁻¹ m⁻¹. A cube of side 0.10 m has one face at x = 0.10 m and the opposite face at x = 0.20 m, and its other faces are parallel to the x-axis. Find the net electric flux through the cube."
Strategy: Only the two faces perpendicular to x contribute.• φ_R = +β(0.20)(0.10)² = +4.0 × 10⁻¹ N C⁻¹ m²• φ_L = −β(0.10)(0.10)² = −2.0 × 10⁻¹ N C⁻¹ m²• Net φ = 2.0 × 10⁻¹ N C⁻¹ m².
Do not add the two face values as positives, which gives 6.0 × 10⁻¹.
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What to remember before solving Electric Flux questions
More in Electrostatics: 3 exam traps and mistakes · 11 formulas · 6 question patterns from its other lessons.
Electric Flux questions from past NEET papers
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Sources
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