📑 Table of Contents
⚡ Class 12 Physics · Chapter 1 · NCERT
Electric Charges
& Fields
Your complete, exam-ready study guide — from basics to board-level mastery. Notes · Formulas · MCQs · PYQs · HOTS · Memory Tricks
🎓 Welcome, Dear Students ! ⚡
You've just opened the gateway to one of the most electrifying chapters of Class 12 Physics! Electric Charges and Fields is not just a chapter — it's the foundation on which all of modern electronics, communication, and technology rests.
Whether your goal is a perfect 35/35 in CBSE Boards, cracking JEE/NEET/CUET, or simply understanding how your phone, fan, and even your nervous system work — this chapter is your launchpad.
Invest 4–5 dedicated hours in this chapter and watch it reward you with easy marks in every exam! Let's light it up! 🔋
CBSE Board: 8–10 Marks
JEE Mains: 2–4 Questions
NEET: 2–3 Questions
CUET: 3–5 Questions
Chapter Overview
This chapter introduces the concept of electric charge — the fundamental property of matter responsible for all electromagnetic phenomena. Starting from static electricity observed thousands of years ago, we build up to Coulomb's Law, the concept of Electric Field, and the powerful tool of Gauss's Law.
📌 Why It Matters
- Foundation for Chapters 2–16 of Class 12
- Direct application in circuits, capacitors, magnetism
- Numericals are formula-based and scoring
- Conceptual questions dominate board papers
🌍 Real-Life Applications
- Lightning rods protect buildings
- Photocopiers use electrostatics
- Air purifiers use electric fields
- Inkjet printers deflect charged droplets
- Thunderstorms — static charge buildup
🗂️ Topics at a Glance
- Electric Charge & its Properties
- Coulomb's Law
- Electric Field & Field Lines
- Electric Dipole
- Electric Flux & Gauss's Law
Most Important Teacher's Notes
⚡ 1. Electric Charge
- A fundamental physical property of matter that causes force in an electromagnetic field.
- Two types: Positive (+) and Negative (−)
- SI unit: Coulomb (C)
- Charge of electron: e = −1.6 × 10⁻¹⁹ C
- Charge of proton: e = +1.6 × 10⁻¹⁹ C
- Like charges repel; unlike charges attract
🔑 2. Properties of Electric Charge
- Additivity: Q = q₁ + q₂ + q₃ + ... (algebraic sum)
- Conservation: Charge can neither be created nor destroyed in an isolated system.
- Quantisation: Q = ne, where n = ±1, ±2, ±3...
⚖️ 3. Coulomb's Law
The electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb's Law
F = k · |q₁q₂| / r²
F = (1/4πε₀) · |q₁q₂| / r²
k = 9 × 10⁹ N·m²/C² | ε₀ = 8.85 × 10⁻¹² C²/N·m²
- Central force — acts along the line joining the two charges
- Obeys Newton's Third Law (action-reaction pair)
- Valid for point charges at rest (electrostatics)
➕ 4. Superposition Principle
The net force on a charge due to many other charges is the vector sum of individual forces.
Superposition
F_total = F₁₂ + F₁₃ + F₁₄ + ...
Each pair of charges interacts independently.
🌐 5. Electric Field
The electric field at a point is the force per unit positive test charge placed at that point.
Electric Field
E = F / q₀ (Vector)
E = kQ / r² (Due to point charge Q)
SI Unit: N/C or V/m | Direction: away from +Q, towards −Q
- Electric field is a vector quantity
- Test charge q₀ must be infinitesimally small
〰️ 6. Electric Field Lines
- Start from positive charges, end at negative charges
- Never intersect each other
- Closer lines = stronger field; farther apart = weaker field
- Always perpendicular to the surface of a conductor at rest
- Do NOT form closed loops
🔗 7. Electric Dipole
A pair of equal and opposite charges (+q and −q) separated by a small distance 2a.
Dipole Moment
p = q × 2a (Vector)
Direction: from −q to +q | SI Unit: C·m
E on Axial Line (r >> a)
E_axial = (1/4πε₀) · 2p/r³
Direction: along dipole moment p
E on Equatorial Line (r >> a)
E_eq = (1/4πε₀) · p/r³
Direction: antiparallel to p
Key Ratio: E_axial = 2 × E_eq (same distance r, r >> a)
🔄 Torque on Dipole in Uniform Electric Field
Torque
τ = p × E = pE sinθ
θ = angle between p and E | Unit: N·m
- τ is maximum when θ = 90° → τ_max = pE
- τ = 0 when θ = 0° (stable equilibrium) or θ = 180° (unstable)
📐 8. Electric Flux
Electric Flux
Φ = E · A · cosθ = E⃗ · A⃗
SI Unit: N·m²/C or V·m | Scalar quantity
- Maximum when E ⊥ surface (θ = 0°)
- Zero when E ∥ surface (θ = 90°)
🔵 9. Gauss's Law & Applications
Gauss's Law
∮ E⃗ · dA⃗ = Q_enc / ε₀
Total flux through any closed surface = enclosed charge / ε₀
| Charge Distribution | Gaussian Surface | Electric Field |
|---|---|---|
| Infinite line charge (λ C/m) | Coaxial cylinder | E = λ / (2πε₀r) |
| Infinite plane sheet (σ C/m²) | Pillbox / Cylinder | E = σ / (2ε₀) |
| Two parallel plates (±σ) | Pillbox | E = σ/ε₀ between plates |
| Charged sphere (outside, r > R) | Sphere radius r | E = Q / (4πε₀r²) |
| Charged sphere (inside, r < R) | Sphere radius r | E = Qr / (4πε₀R³) |
NCERT Important Definitions
Definition
Electric Charge
A fundamental physical property of matter that causes it to experience a force when placed in an electromagnetic field. It is the source of all electric and magnetic phenomena.
Definition
Coulomb's Law
The electrostatic force between two stationary point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. F = kq₁q₂/r²
Definition
Electric Field
The region around a charge in which another charge experiences an electrostatic force. Quantitatively, E = F/q₀, where q₀ is a small positive test charge.
Definition
Electric Field Lines
Imaginary curves drawn in an electric field such that the tangent at any point gives the direction of the electric field at that point. Denser lines indicate stronger field.
Definition
Electric Dipole
A system of two equal and opposite charges (+q and −q) separated by a small distance 2a. The dipole moment p = q(2a), directed from negative to positive charge.
Definition
Electric Flux (Φ)
The total number of electric field lines passing normally through a given surface. Φ = E·A·cosθ. SI Unit: N·m²/C.
Definition
Gauss's Law
The total electric flux through any closed surface is equal to 1/ε₀ times the total charge enclosed within the surface. ∮E⃗·dA⃗ = Q_enc/ε₀
Definition
Quantisation of Charge
Electric charge exists only in discrete integral multiples of the elementary charge e = 1.6 × 10⁻¹⁹ C. Thus Q = ne, where n is an integer.
Definition
Conservation of Charge
The total electric charge in an isolated system remains constant. Charge can neither be created nor destroyed, only transferred from one body to another.
Text Diagrams & Visual Aids
⊕ Charge Interaction
(+q) ←————F————→ (+q) [REPULSION — Like Charges]
(+q) ————F→ ←F———— (−q) [ATTRACTION — Unlike Charges]
Arrow (→) shows direction of force on each charge.
〰️ Electric Field Line Patterns
ISOLATED POSITIVE CHARGE: ISOLATED NEGATIVE CHARGE:
↑ ↑ ↑ ↑ ↑ ↑
← (+) → Lines radiate OUTWARD → (−) ← Lines converge INWARD
↓ ↓ ↓ ↓ ↓ ↓
DIPOLE (+q and −q):
____
↗ / \ ↘
(+q) (−q) Lines arc FROM +q TO −q
↘ \____/ ↗
📏 Electric Dipole
2a
(−q) ←—————→ (+q)
|←—p—→|
p = q × 2a (vector from −q to +q)
AXIAL LINE: along axis joining the charges
EQUATORIAL LINE: perpendicular bisector of the dipole
🔵 Gaussian Surfaces
SPHERICAL SURFACE (around point charge Q):
_____
/ • \ ←— Q at centre
| ↑ |
| ← → | E points radially outward
| ↓ |
\_______/
∮ E·dA = Q/ε₀ → E × 4πr² = Q/ε₀ → E = Q/(4πε₀r²)
CYLINDRICAL SURFACE (around infinite line charge λ):
┌─────────────────┐
│ →→→→→→→→→→→ │ λ C/m
└─────────────────┘
E × 2πrl = λl/ε₀ → E = λ/(2πε₀r)
Concept Mind Map
⚡ Electric Charges & Fields
Electric Charge
+ve & −ve Charges
Quantisation Q=ne
Conservation
Additivity
Coulomb's Law F=kq₁q₂/r²
Superposition Principle
Electric Field E=F/q₀
Field Line Properties
Electric Dipole p=q·2a
Axial Field ∝ 2p/r³
Equatorial Field ∝ p/r³
Torque τ=pE sinθ
Electric Flux Φ=E·A·cosθ
Gauss's Law ∮E·dA=Q/ε₀
Line Charge E=λ/2πε₀r
Plane Sheet E=σ/2ε₀
Memory Tricks & Shortcuts
🧠 Properties of Charge
"A Careful Queen" = Additivity + Conservation + Quantisation
Remember: Charge follows ACQ!
Remember: Charge follows ACQ!
🧠 Coulomb's Law
F = k · q₁q₂ / r² → "Force = Konstant × charges ÷ (radius)²"
k = 9 × 10⁹ → "Nine Billion"
k = 9 × 10⁹ → "Nine Billion"
🧠 Axial vs Equatorial
Axial = "End-On" = 2p/r³ (2× bigger)
Equatorial = "Broad-Side" = p/r³
Trick: "Axial is Ahead — gets 2!"
Equatorial = "Broad-Side" = p/r³
Trick: "Axial is Ahead — gets 2!"
🧠 Field Lines — PENCIL Rule
Positive → start | End at negative
Never cross each other
Closer = stronger field
Infinitely long for isolated charges
Lines ⊥ to conductor surface
Never cross each other
Closer = stronger field
Infinitely long for isolated charges
Lines ⊥ to conductor surface
🧠 Gauss's Law Quick Recall
"Total Flux = Total Charge Inside / ε₀"
Imagine a bubble around charges — it senses only what's inside. Outside charges cancel out!
Imagine a bubble around charges — it senses only what's inside. Outside charges cancel out!
🧠 Units Trick
Electric Field E: N/C = V/m (both are exactly same!)
Flux Φ: N·m²/C = V·m
Flux Φ: N·m²/C = V·m
Did You Know? Lightning is a giant electrostatic discharge. A single lightning bolt carries ~1 billion volts and 20,000 amperes — all explained by principles in this very chapter!
Complete Formula Sheet
1. Quantisation of Charge
Q = ne (n = ±1, ±2, ±3, ...)
e = 1.6 × 10⁻¹⁹ C
2. Coulomb's Law
F = (1/4πε₀) × |q₁q₂| / r²
k = 9 × 10⁹ N·m²/C² | ε₀ = 8.85 × 10⁻¹² C²/N·m²
3. Electric Field (point charge)
E = (1/4πε₀) × Q/r²
Unit: N/C or V/m
4. Dipole Moment
p = q × 2a (from −q → +q)
Unit: C·m
5. E — Axial Point (r >> a)
E_axial = (1/4πε₀) × 2p/r³
Direction: along dipole moment p
6. E — Equatorial Point (r >> a)
E_eq = (1/4πε₀) × p/r³
Direction: antiparallel to p
7. Torque on Dipole
τ = pE sinθ (or τ = p⃗ × E⃗)
Max when θ=90° → τ_max = pE
8. Electric Flux
Φ = E × A × cosθ = E⃗ · A⃗
Unit: N·m²/C or V·m
9. Gauss's Law
∮ E⃗ · dA⃗ = Q_enc / ε₀
Works for any closed surface
10. E — Infinite Line Charge
E = λ / (2πε₀r)
λ = linear charge density (C/m)
11. E — Infinite Plane Sheet
E = σ / (2ε₀)
σ = surface charge density (C/m²) | independent of distance!
12. E — Two Parallel Plates
E = σ / ε₀ (between) | E = 0 (outside)
Only between plates; cancels outside
NCERT Exercise — Key Q&A
Q 1.1
What is the force between two small charged spheres having charges of 2 × 10⁻⁷ C and 3 × 10⁻⁷ C placed 30 cm apart in air?
Given: q₁ = 2 × 10⁻⁷ C, q₂ = 3 × 10⁻⁷ C, r = 0.30 m
F = (9 × 10⁹ × 2 × 10⁻⁷ × 3 × 10⁻⁷) / (0.30)²
F = (9 × 10⁹ × 6 × 10⁻¹⁴) / 0.09
F = 6 × 10⁻³ N (Repulsive)
F = (9 × 10⁹ × 2 × 10⁻⁷ × 3 × 10⁻⁷) / (0.30)²
F = (9 × 10⁹ × 6 × 10⁻¹⁴) / 0.09
F = 6 × 10⁻³ N (Repulsive)
Q 1.2
The electrostatic force on a small sphere of charge 0.4 μC due to another of charge −0.8 μC is 0.2 N. (a) Find the distance. (b) Find force on the second sphere.
(a) r² = kq₁q₂/F = (9×10⁹ × 0.4×10⁻⁶ × 0.8×10⁻⁶)/0.2 = 0.0144 → r = 0.12 m = 12 cm
(b) By Newton's Third Law: 0.2 N (attractive, toward first sphere)
(b) By Newton's Third Law: 0.2 N (attractive, toward first sphere)
Q 1.8
A polythene piece rubbed with wool has a negative charge of 3 × 10⁻⁷ C. Estimate the number of electrons transferred.
n = Q/e = (3 × 10⁻⁷) / (1.6 × 10⁻¹⁹)
n = 1.875 × 10¹² electrons (transferred from wool to polythene)
n = 1.875 × 10¹² electrons (transferred from wool to polythene)
Q 1.12
A charge of 8 mC is at the origin. Calculate work done in taking −2 × 10⁻⁹ C from P(0,0,3 cm) to Q(0,4 cm,0) via R(0,6 cm,9 cm).
Electric force is conservative — work depends only on initial and final positions.
V_P = kQ/r_P = (9×10⁹ × 8×10⁻³)/0.03 = 2.4 × 10⁹ V
V_Q = kQ/r_Q = (9×10⁹ × 8×10⁻³)/0.04 = 1.8 × 10⁹ V
W = q(V_Q − V_P) = (−2×10⁻⁹)(−0.6×10⁹) = 1.27 J
V_P = kQ/r_P = (9×10⁹ × 8×10⁻³)/0.03 = 2.4 × 10⁹ V
V_Q = kQ/r_Q = (9×10⁹ × 8×10⁻³)/0.04 = 1.8 × 10⁹ V
W = q(V_Q − V_P) = (−2×10⁻⁹)(−0.6×10⁹) = 1.27 J
Previous Year Board Questions
Questions below are frequently repeated. Mastering these guarantees marks in your board exam!
✅ 1-Mark Questions
Q. Write the SI unit of electric flux.
Ans: N·m²/C (Newton metre² per Coulomb) or V·m (Volt metre)
Q. Two charges 4q and q are placed at distance r. Where should a third charge Q be placed for system equilibrium?
Ans: At distance r/3 from q (or 2r/3 from 4q). Q must be negative.
Q. Can two electric field lines ever intersect? Give reason.
Ans: No. Intersection would mean two directions of E at the same point — physically impossible.
✅ 2-Mark Questions
Q. State Gauss's law. Write the expression for E due to an infinitely long straight wire of linear charge density λ.
Ans: Gauss's Law: ∮E·dA = Q_enc/ε₀
For infinite line charge: E = λ/(2πε₀r), where r is perpendicular distance from wire.
For infinite line charge: E = λ/(2πε₀r), where r is perpendicular distance from wire.
Q. Define electric dipole moment. Write its SI unit. Is it scalar or vector?
Ans: p = q × 2a. SI unit: C·m. It is a vector — directed from −q to +q.
✅ 3-Mark Questions
Q. Derive expression for electric field on the equatorial line of an electric dipole (r >> a).
Ans: Distance from each charge to point P on equatorial line: d = √(r² + a²)
E₊ = E₋ = kq/(r² + a²). Components along equatorial line cancel; along dipole direction add:
E_eq = 2kq(r² + a²)⁻¹ × cosθ, cosθ = a/√(r² + a²)
E_eq = 2kqa/(r² + a²)^(3/2) = kp/(r² + a²)^(3/2)
For r >> a: E_eq = kp/r³ = p/(4πε₀r³) (antiparallel to p)
E₊ = E₋ = kq/(r² + a²). Components along equatorial line cancel; along dipole direction add:
E_eq = 2kq(r² + a²)⁻¹ × cosθ, cosθ = a/√(r² + a²)
E_eq = 2kqa/(r² + a²)^(3/2) = kp/(r² + a²)^(3/2)
For r >> a: E_eq = kp/r³ = p/(4πε₀r³) (antiparallel to p)
✅ 5-Mark Question
Q. (a) State Gauss's Law. (b) Derive E due to uniformly charged infinite plane sheet. (c) Find E between and outside two parallel sheets with ±σ.
(a) ∮E·dA = Q_enc/ε₀
(b) Cylindrical Gaussian surface of cross-section A: Curved surface flux = 0, two end caps give 2EA = σA/ε₀ → E = σ/(2ε₀)
(c)(i) Between plates: both fields add → E = σ/ε₀
(c)(ii) Outside both plates: fields cancel → E = 0
(b) Cylindrical Gaussian surface of cross-section A: Curved surface flux = 0, two end caps give 2EA = σA/ε₀ → E = σ/(2ε₀)
(c)(i) Between plates: both fields add → E = σ/ε₀
(c)(ii) Outside both plates: fields cancel → E = 0
✅ Case-Based Question
Q. A lightning conductor is a metallic rod fixed at top of a building, connected to earth. Answer: (i) What property of field lines keeps the conductor equipotential? (ii) Why is a pointed rod preferred? (iii) SI unit of electric field intensity? (iv) Is charge distribution uniform on the rod?
(i) Field lines are always perpendicular to conductor surface.
(ii) At sharp points, σ is very high → very strong E → ionisation of air → charge leaks (corona discharge).
(iii) N/C or V/m
(iv) No — charge density is higher at sharp points/tips than at flat regions.
(ii) At sharp points, σ is very high → very strong E → ionisation of air → charge leaks (corona discharge).
(iii) N/C or V/m
(iv) No — charge density is higher at sharp points/tips than at flat regions.
30 Most Important Board Exam Questions
- State Coulomb's Law and write its mathematical expression.
- What is electric field? Define its SI unit.
- Why can two electric field lines never intersect?
- Define electric flux and give its SI unit.
- State and prove Gauss's Law.
- Derive E on the axial line of an electric dipole.
- Derive E on the equatorial line of a dipole.
- Compare E on axial and equatorial positions of a dipole.
- What is a Gaussian surface? State its properties.
- Find E due to infinite plane sheet using Gauss's Law.
- Find E due to infinitely long charged wire.
- Explain quantisation of electric charge with examples.
- Explain conservation of charge with examples.
- What is superposition principle? How is it applied?
- Find the torque on a dipole in uniform electric field.
- Explain 6 properties of electric field lines.
- Three charges at vertices of equilateral triangle — find net force.
- What is the significance of negative electric flux?
- How does E due to a point charge vary with distance?
- Define linear, surface, and volume charge density.
- Why is the electric field inside a conductor zero?
- Sketch field lines for a dipole and an isolated charge.
- Two equal and opposite charges — what is the net charge?
- How does Coulomb's force change in a medium vs. vacuum?
- Derive E inside and outside a uniformly charged sphere.
- Define dielectric constant (εᵣ) and its effect on Coulomb's force.
- Explain the principle of a Van de Graaff generator.
- What is meant by "test charge" in the definition of electric field?
- If total flux through a closed surface is zero, is there no charge inside?
- A charge Q is enclosed in a cube — find flux through one face.
Ans Q.29: Not necessarily — equal +ve and −ve charges can give zero net flux. Net flux = 0 ≠ no enclosed charge.
Ans Q.30: By symmetry, flux through one face = Q/(6ε₀)
Ans Q.30: By symmetry, flux through one face = Q/(6ε₀)
Quick Revision Notes
⚡ ChargeSI unit: Coulomb (C) | e = 1.6×10⁻¹⁹ C
🔑 PropertiesAdditivity, Conservation, Quantisation (ACQ)
⚖️ CoulombF = kq₁q₂/r² | k = 9×10⁹
➕ SuperpositionVector sum of individual forces
🌐 FieldE = F/q₀ = kQ/r² | N/C or V/m
〰️ Lines+→−, never cross, ⊥ conductor
🔗 Dipolep = q·2a | from −q to +q
📏 Axial E= 2kp/r³ (along p)
📐 Equatorial= kp/r³ (antiparallel)
🔄 Torqueτ = pE sinθ | Max θ=90°
📊 FluxΦ = E·A·cosθ | N·m²/C
🔵 Gauss∮E·dA = Q_enc/ε₀
📡 LineE = λ/(2πε₀r)
🔲 SheetE = σ/(2ε₀)
🔳 PlatesE = σ/ε₀ between | 0 outside
🌕 Sphere r>RE = kQ/r²
🌕 Sphere r<RE = kQr/R³
ε₀8.85 × 10⁻¹² C²/N·m²
HOTS — Higher Order Thinking Questions
🧠 HOTS — Level 1
Q. If the distance between two equal charges is doubled and each charge is also doubled, how does the force change?
F' = k(2q)(2q)/(2r)² = k·4q²/4r² = kq²/r² = F
The force remains unchanged! Both effects cancel perfectly.
The force remains unchanged! Both effects cancel perfectly.
🧠 HOTS — Level 2
Q. A point charge +Q is placed at the centre of a cube. What is the electric flux through one face? Through two faces?
Total flux = Q/ε₀. By symmetry: one face = Q/(6ε₀), two faces = Q/(3ε₀)
🧠 HOTS — Level 3
Q. Can E = 0 where V ≠ 0? Can V = 0 where E ≠ 0? Give examples.
Yes to both!
(i) E=0, V≠0: Centre of a uniformly charged ring — E cancels, V = kQ/R ≠ 0.
(ii) V=0, E≠0: Midpoint between +q and −q — potentials cancel, but E points from +q to −q.
(i) E=0, V≠0: Centre of a uniformly charged ring — E cancels, V = kQ/R ≠ 0.
(ii) V=0, E≠0: Midpoint between +q and −q — potentials cancel, but E points from +q to −q.
🧠 HOTS — Level 4
Q. A charge Q is uniformly distributed on a ring of radius R. Find E at the centre and at a point on the axis at distance x.
At centre: E = 0 (by symmetry, each element cancels)
On axis: E = kQx/(R² + x²)^(3/2) | Maximum at x = R/√2
On axis: E = kQx/(R² + x²)^(3/2) | Maximum at x = R/√2
🧠 HOTS — Level 5
Q. Two identical metal spheres A (+3Q) and B (−Q) are brought into contact and then separated. What are the final charges?
Total charge = 3Q + (−Q) = 2Q. Identical spheres share equally: A = +Q, B = +Q
Common Mistakes to Avoid
Mistake 1: Confusing force (F) with field (E). Force needs two charges; field exists due to one. E = F/q₀.
Mistake 2: Treating E as scalar. E is a VECTOR — always state its direction.
Mistake 3: Writing dipole direction from +q to −q. Correct: −q to +q.
Mistake 4: Forgetting Coulomb's Law uses product of both charges — if either is zero, force is zero.
Mistake 5: Confusing axial and equatorial fields. Axial = 2p/r³ (along p); Equatorial = p/r³ (antiparallel to p).
Mistake 6: Saying E inside a conductor is non-zero. E is always zero for conductors in electrostatic equilibrium.
Mistake 7: Mixing cm and m in numericals. Always convert distance to metres (m) before substituting.
Mistake 8: Using E = σ/(2ε₀) between two parallel plates. Between plates, both sheets contribute: E = σ/ε₀.
Self-Assessment Quiz — 20 MCQs
Q1. The SI unit of electric charge is:
C = A·s | Charge = Current × Time
Q2. The value of 1/4πε₀ is:
Standard value: k = 9 × 10⁹ N·m²/C²
Q3. Two equal positive charges at vertices of equilateral triangle. Electric field at third vertex (no charge) points:
By symmetry, equal fields give resultant pointing away from midpoint of +q, +q.
Q4. Electric flux through a closed surface depends on:
Gauss's Law: Φ = Q_enc/ε₀ — only enclosed charge matters.
Q5. Torque on dipole in uniform field is maximum when angle between p and E is:
τ = pE sinθ → max when sinθ = 1 i.e. θ = 90°
Q6. The electric field inside a conducting sphere with charge Q is:
E = 0 inside any conductor in electrostatic equilibrium.
Q7. Which is NOT a property of electric field lines?
Electric field lines do NOT form closed loops (unlike magnetic field lines).
Q8. The direction of electric dipole moment is from:
By convention, p points from negative to positive charge.
Q9. Electric field due to infinite plane sheet (σ C/m²) is:
From Gauss's Law: E = σ/(2ε₀) on each side of the sheet.
Q10. If distance between two charges is halved, the Coulomb force becomes:
F ∝ 1/r² → if r → r/2, F → 4F
Q11. Which quantity has SI unit V·m?
Φ = E·A → (V/m)·m² = V·m
Q12. On the equatorial line of an electric dipole, field direction is:
E_eq is antiparallel to p — very common exam question!
Q13. The charge on an electron is:
e = −1.6 × 10⁻¹⁹ C | 9.1 × 10⁻³¹ is the mass of electron, not charge!
Q14. A charge Q at the centre of a sphere is shifted to one side (still inside). Flux through sphere:
Flux depends only on enclosed charge, not its position: Φ = Q/ε₀
Q15. For a point outside a uniformly charged hollow shell, the shell behaves as:
By Gauss's Law, E = kQ/r² outside — same as a point charge Q at centre.
Q16. Electric field lines are denser where the field is:
Density of lines ∝ magnitude of E. More lines = stronger field.
Q17. Which law is equivalent to Coulomb's Law but more general?
Gauss's Law is more powerful — Coulomb's Law can be derived from it.
Q18. Number of electrons making up −1 C of charge is:
n = 1/(1.6 × 10⁻¹⁹) = 6.25 × 10¹⁸ electrons
Q19. Electric field at distance r from an infinite line charge varies as:
E = λ/(2πε₀r) — varies as 1/r for infinite line charge (unlike 1/r² for point charge).
Q20. An electric dipole in a non-uniform electric field experiences:
Non-uniform field: both net force AND torque act. Uniform field: only torque (net force = 0).
Board Exam Preparation Tips
- Master the 12 formulas — write them on a sticky note and review daily. 50% of marks come from formula-based numericals.
- Practice derivations of Gauss's Law applications (plane sheet, line charge, sphere) at least 3 times each — guaranteed 5-mark questions.
- Draw neat diagrams for every answer involving dipoles, field lines, or Gaussian surfaces. CBSE awards separate marks for diagrams.
- Memorise the E_axial vs E_equatorial ratio (2:1) and their directions — appears in almost every year's paper.
- Time yourself: A 5-mark numerical should take maximum 7–8 minutes. Practice under time pressure.
- Attempt MCQs daily: This chapter has 4–5 MCQs in competitive exams. Speed and accuracy both matter.
- Revisit NCERT Examples: Board questions often reword NCERT examples. Solve every single one.
Chapter Summary
Electric charge is a fundamental property of matter, existing in two types (+ve and −ve), quantised as Q = ne and conserved in isolated systems. Coulomb's Law gives the force between stationary charges: F = kq₁q₂/r². The superposition principle allows us to find net forces from multiple charges by vector addition.
The Electric Field (E = F/q₀) is a vector field representing force per unit positive charge. Electric field lines visualise this field — starting on positive, ending on negative charges, never crossing. An Electric Dipole (p = q·2a) produces fields along axial (2p/r³) and equatorial (p/r³) lines, with torque τ = pE sinθ in a uniform field.
Electric Flux (Φ = E·A·cosθ) quantifies field lines through a surface. Gauss's Law (∮E·dA = Q_enc/ε₀) elegantly connects flux to enclosed charge, enabling easy calculation of E for symmetric charge distributions. These results are the bedrock of all further chapters in electrostatics and electrodynamics.
🙏 You've Got This!
Every formula you've memorised, every diagram you've drawn, and every MCQ you've solved brings you one step closer to your goal. Electric Charges and Fields is the language the universe uses to describe how matter interacts at the most fundamental level.
Revise the formula sheet daily, attempt past papers under timed conditions, and never skip the derivations — they are guaranteed marks. Remember: consistency beats cramming every single time.
✨ Practice with purpose. Revise with confidence. Perform with excellence. All the best for your exams! ⚡
— Your teachers at Jnaanangkur – The Learning Hub
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