Electric Charges & Fields — Complete Study Guide
CBSE + NEET Physics · Class 12 · Chapter 1

Electric Charges
& Fields

The most visual, intuitive, and exam-oriented guide — built for weak and average students who want to score big.

11
Topics Covered
30+
Practice Questions
3
Difficulty Levels
35%
NEET Weight
Scroll
01

NCERT Chapter Map

★ Must Study
Coulomb's Law
Force between charges, vector form, superposition principle. Most tested in NEET.
35%
★ Must Study
Electric Field
Definition, formula, field due to point charge, field lines, properties.
28%
★ Must Study
Electric Dipole
Dipole moment, field on axial & equatorial points, torque, potential energy.
18%
◈ Important
Gauss's Law
Electric flux, Gauss's theorem, applications to shell, cylinder, plane.
12%
◈ Important
Charge Properties
Quantization (q=ne), conservation, additivity, charging methods.
7%
· Optional
Continuous Charge
Linear (λ), surface (σ), volume (ρ) charge densities. For CBSE only.
~0%
💡 Study order recommendation: Charge properties → Coulomb's Law → Electric Field → Field Lines → Dipole → Electric Flux → Gauss's Law. Don't skip steps!
02

Concept Building

💧
Think of charge like water in a tank. Positive charge = water above normal level. Negative charge = water below normal level. When two tanks connect (objects touch), water flows until balanced — that flow IS electric current. This is why charge always seeks equilibrium!

Three Properties of Charge — Exam Goldmine

🔢
Quantization
q = ne
Charge exists only in exact multiples of e. You can't have 1.5 electrons worth of charge — nature doesn't allow fractions!
e = 1.6 × 10⁻¹⁹ C
n = 1, 2, 3, ... (integer)
♾️
Conservation
ΣQ = constant
Charge can't be created or destroyed. When you rub a comb, electrons transfer — the total charge of (comb + hair) stays exactly zero.
Friction: 0 → −3e + 3e
Total always = 0
Additivity
Q = q₁ + q₂ + ...
Total charge is the simple algebraic sum. Treat charges like signed numbers — positives and negatives cancel each other out.
+5μC + (−3μC) + 2μC
= +4μC total

Charging Methods

🔥
Friction
Electrons transfer by rubbing. Both bodies get charged with opposite signs. Example: rubber rod + fur → rod gets −ve.
CBSE asks: which body gains/loses electrons and why.
🤝
Conduction
Direct contact between charged and uncharged body. Charge distributes. Both end up with same sign charge.
Key: bodies must TOUCH. Final charge = same sign as charging body.
Induction
Charged body brought NEAR (not touching). Opposite charge appears on nearer side. Grounding makes charge permanent.
Key: No touch! Induced charge is always OPPOSITE in sign.
03

Electric Field Lines

🌊
Field lines are like rivers on a map. Direction = where the current flows (where a +ve test charge would move). Density = speed/strength (crowded lines = strong field, spread-out = weak field). Rivers never cross each other — neither do field lines!
+
Positive Charge (+q)
Lines radiate outward in all directions
Negative Charge (−q)
Lines converge inward from all directions
+
Dipole (+q and −q)
Curved lines from + to −; closed-looking loops
+ + N.P.
Two Equal +ve Charges
Lines repel; neutral point (N.P.) in between

8 Properties of Field Lines NEETCBSE

P1
Start & End: Always start on positive charge and end on negative charge (or go to infinity from an isolated +ve charge).
P2
Never Cross: Two field lines NEVER intersect. If they did, two directions of E would exist at that point — physically impossible.
P3
Density = Strength: Crowded (dense) lines mean strong electric field. Spread-out (sparse) lines mean weak field.
P4
Perpendicular to Conductors: Field lines always meet a conductor surface at 90°. If any tangential component existed, surface charges would keep moving — conductor would never be in equilibrium.
P5
No Closed Loops: Electric field lines are NOT closed loops (unlike magnetic field lines). This is because the electric field is non-conservative... actually it IS conservative — lines don't close!
P6
Tangent = Direction: The tangent drawn at any point on a field line gives the direction of E at that point.
P7
Neutral Point: Between two equal and similar charges, a neutral point exists where E = 0. No field line passes through it.
P8
Inside Conductor = Zero: No field lines exist inside a conductor. E = 0 inside. All charge resides on the outer surface.
04

Coulomb's Law

Adjust the sliders to see how force changes with charge and distance in real-time. This is the most important formula in the chapter.

+q₁
−q₂
F = kq₁q₂/r²  =  (1/4πε₀) × q₁q₂/r²
q₁ (μC) 5 μC
q₂ (μC) 5 μC
Distance r (m) 1.0 m
Force F
2.25 N
If r doubles
0.56 N
If q₁ × 2
4.50 N
Nature
Attractive
Constants to Memorise
k (Coulomb's constant)9 × 10⁹ N·m²/C²
ε₀ (permittivity)8.85 × 10⁻¹² C²/N·m²
e (electron charge)1.6 × 10⁻¹⁹ C
1 μC10⁻⁶ C
Inverse Square Law — Quick Facts
Distance doubles → Force becomes ¼ (F × 1/4)
Distance triples → Force becomes 1/9
Distance halves → Force becomes
In medium: Force reduces by factor εᵣ
Memory: Same inverse-square law as gravity. But electric force can be attractive OR repulsive!
05

Electric Dipole

🧲
A dipole is like a tiny bar magnet made of charges. One end is + (north), other end is − (south). The strength of this "charge magnet" is the dipole moment (p). Water molecules are real-life dipoles — that's why they dissolve ionic compounds!
Structure of an Electric Dipole
−q
negative
p⃗ direction →
+q
+
positive
←————— 2a (dipole length) —————→
p = q × 2a  |  Unit: C·m  |  Direction: −q → +q
📍 Axial Point (on the axis)
E = (1/4πε₀) × 2pr/(r²−a²)²
When r >> a: E = 2kp/r³
Direction: SAME as dipole moment p⃗
Decreases as 1/r³ (faster than point charge)
📍 Equatorial Point (⊥ bisector)
E = (1/4πε₀) × p/(r²+a²)^(3/2)
When r >> a: E = kp/r³
Direction: OPPOSITE to dipole moment p⃗
Exactly half of E_axial at same distance r
🏆
E_axial = 2 × E_equatorial  (at same distance r, when r >> a) This comparison is asked almost every year in NEET. Memorize it. Never confuse the directions — axial is same as p⃗, equatorial is opposite.
Torque on Dipole in Uniform E
τ = pE sinθ = p⃗ × E⃗
Max torque at θ = 90° → τ_max = pE
Zero torque at θ = 0° or 180° (equilibrium)
Potential Energy of Dipole
U = −pE cosθ = −p⃗·E⃗
θ=0°: U = −pE (stable equilibrium, min PE)
θ=180°: U = +pE (unstable, max PE)
06

Electric Flux & Gauss's Law

Think of electric flux like raindrops passing through a window. Flux = how many "field lines" pass through a surface. Tilt the window and fewer drops pass (cosθ factor). Gauss's Law says: the total "rain" through any closed surface depends ONLY on how many clouds (charges) are inside — not the size or shape of the surface!
Electric Flux (Φ)
Φ = E · A · cosθ
θ = angle between E⃗ and area normal n̂
For non-uniform field: Φ = ∮E⃗·dA⃗
Unit: N·m²/C  OR  V·m (both same)
When θ = 90°, flux = 0 (E parallel to surface). When θ = 0°, flux = max (E perpendicular to surface).
Gauss's Law
∮E⃗·dA⃗ = q_enclosed / ε₀
Total flux through ANY closed surface = charge enclosed / ε₀
⚠️ The MOST common NEET trap: Flux does NOT depend on the size or shape of the Gaussian surface — only on the enclosed charge!

Gauss's Law Applications

🔵
Spherical Shell
Outside (r > R): E = kQ/r²
Inside (r < R): E = 0
All charge on surface. Inside = shielded. This is why a car is safe during lightning (Faraday cage)!
📏
Infinite Line Charge
E = λ / (2πε₀r)
E decreases as 1/r (not 1/r²). λ = linear charge density in C/m. Radially outward for +ve λ.
📋
Infinite Plane Sheet
E = σ / (2ε₀)
E is same at all distances! Independent of r. σ = surface charge density. Between two opposite sheets: E = σ/ε₀.
07

Formula Sheet

★ Coulomb's Law
ForceF = kq₁q₂/r² = q₁q₂/4πε₀r²N (Newton)
k constantk = 9 × 10⁹ N·m²/C²Memorize!
In mediumF_m = F_air / εᵣεᵣ ≥ 1
★ Electric Field
DefinitionE = F / q₀N/C or V/m
Point chargeE = kq / r²radial
Inside conductorE = 0Always!
◈ Charge Properties
Quantizationq = nen = integer
e (electron)1.6 × 10⁻¹⁹ CMemorize!
ε₀8.85 × 10⁻¹² C²/N·m²Memorize!
★ Electric Dipole
Dipole momentp = q × 2aC·m; from −→+
E_axial (r>>a)2kp / r³same as p⃗
E_equatorial (r>>a)kp / r³opp. to p⃗
Golden ruleE_axial = 2 × E_eq★ NEET!
Torqueτ = pE sinθmax at θ=90°
PE of dipoleU = −pE cosθmin at θ=0°
◈ Gauss's Law
Electric fluxΦ = EA cosθN·m²/C
Gauss's law∮E·dA = q/ε₀enclosed q only
Line chargeE = λ / 2πε₀r∝ 1/r
Plane sheetE = σ / 2ε₀const., no r!
🧠 Memory Tricks
"Distance doubles = Force quarters" — F ∝ 1/r², so doubling r gives F/4
"Axial = 2 × Equatorial" — The golden dipole rule, never forget!
"Flux = Enclosed charge only" — Shape/size of surface doesn't matter
"E inside conductor = ZERO" — Always, no exceptions in electrostatics
08

Problem Solving Strategy

1
🔍
Identify
Write down all given values and what is asked. Convert units (μC → C). Never skip this step!
2
✏️
Draw Diagram
Sketch charges with positions, distances and directions. This alone prevents 80% of sign errors.
3
📋
Choose Formula
Force? → Coulomb's law. Field? → E=kq/r². Dipole? → Check axial or equatorial. Flux? → Gauss.
4
🎯
Solve Smart
Magnitude first, then direction. For vectors: break into x-y components, add, find resultant.
⚠️ The silent killer in this chapter: Forgetting to use vectors in superposition problems. Always resolve forces into x and y components separately. This separates 85+ scorers from 65 scorers.
09

Practice Questions

Q1
What is the charge on an electron? What is the SI unit of charge?
−1.6 × 10⁻¹⁹ C. The SI unit is Coulomb (C). This is the smallest unit of free charge — directly from quantization!
Q2
A body has a charge of −3.2 × 10⁻¹⁸ C. How many excess electrons does it have?
n = q/e = 3.2×10⁻¹⁸ / 1.6×10⁻¹⁹ = 20 electrons. The body has gained 20 extra electrons, making it negatively charged.
Q3
Can a body have a charge of 1.5 × 10⁻¹⁹ C? Justify your answer.
No! By quantization: q = ne. Here n = 1.5×10⁻¹⁹/1.6×10⁻¹⁹ = 0.9375 — not an integer. Only integer multiples of e are allowed. This charge is NOT possible.
Q4
In which direction do electric field lines point for a negative point charge?
Field lines point INWARD — towards the negative charge from all directions. Remember: positive test charge would move TOWARD a negative charge.
Q5
What is the electric field inside a hollow conducting sphere?
E = 0 inside. All charge resides on the outer surface. This is a direct application of Gauss's law (no enclosed charge = no flux = no field). This is tested very often!
Q6
Two charges repel each other. What can you say about the signs of the charges?
Both must be of the SAME sign — either both positive or both negative. Like charges repel, unlike charges attract. This is the fundamental rule.
Q7
Name the method of charging where the charged body does NOT touch the body being charged.
Charging by INDUCTION. The charged body is brought near (not touching). Charge separation occurs in the neutral body. Grounding makes the induced charge permanent.
Q8
What is the value of the Coulomb constant k? Express it also in terms of ε₀.
k = 9 × 10⁹ N·m²/C². In terms of ε₀: k = 1/(4πε₀), where ε₀ = 8.85 × 10⁻¹² C²/N·m² is the permittivity of free space (vacuum).
Q9
Can two electric field lines ever intersect each other? Why or why not?
No, NEVER. If two lines intersected, there would be two directions of E at the intersection point. That is physically impossible — E has a unique direction at every point in space.
Q10
What is the direction of the dipole moment vector p?
From NEGATIVE charge to POSITIVE charge (−q → +q). This is by convention. Students often confuse this with the direction of E-field between the charges (which goes from + to −).
Q1
Two charges +2μC and −2μC are placed 30 cm apart in vacuum. Find the force between them.
F = k|q₁q₂|/r² = 9×10⁹ × 2×10⁻⁶ × 2×10⁻⁶ / (0.3)² = 9×10⁹ × 4×10⁻¹² / 0.09 = 0.4 N. Force is ATTRACTIVE (unlike charges). Always check sign of force!
Q2
An electric dipole has charges ±4μC separated by 2 cm. Find the dipole moment.
p = q × 2a = 4×10⁻⁶ × 2×10⁻² = 8×10⁻⁸ C·m = 80 nC·m. Direction: from −4μC to +4μC. Don't forget to include direction in your answer!
Q3
Find the electric field at a point 30 cm from a point charge of 5μC in vacuum.
E = kq/r² = 9×10⁹ × 5×10⁻⁶ / (0.3)² = 45000 / 0.09 = 5×10⁵ N/C. Direction: radially away from the positive charge.
Q4
What is the electric flux through a closed surface enclosing a charge of 8.85 nC?
Φ = q/ε₀ = 8.85×10⁻⁹ / 8.85×10⁻¹² = 1000 N·m²/C. Direct application of Gauss's law — shape of surface doesn't matter at all!
Q5
An electric field of 1000 N/C acts on a dipole with p = 2×10⁻⁸ C·m. Find the maximum torque.
τ_max = pE (at θ = 90°) = 2×10⁻⁸ × 1000 = 2×10⁻⁵ N·m. Remember: maximum torque at θ=90°, minimum torque (zero) at θ=0° or 180°.
Q6
What is flux through a cube of side 10 cm with charge 8.85μC at its centre?
Φ_total = q/ε₀ = 8.85×10⁻⁶/8.85×10⁻¹² = 10⁶ N·m²/C. Per face = 10⁶/6 N·m²/C. Key: total flux depends ONLY on enclosed charge, NOT on size or shape!
Q7
The force between two charges is F in air. What will be the force in a medium of εᵣ = 4?
F_medium = F_air / εᵣ = F/4. A dielectric medium reduces electrostatic force by factor εᵣ. Medium gets polarized and weakens the original field.
Q8
Two equal conducting spheres with charges +6μC and −2μC touch and separate. Find final charge.
Total charge = +6−2 = +4μC. After contact with identical spheres, charge distributes equally: each sphere gets +2μC. Works ONLY for identical (same-size) spheres!
Q9
State whether a charge of 0.8×10⁻¹⁸ C is possible.
YES. n = 0.8×10⁻¹⁸/1.6×10⁻¹⁹ = 5 — exactly 5e, a valid integer multiple. Charge IS quantized and this is a valid charge. Always check if n is an integer!
Q10
Two equal charges are placed 1m apart. Where should a third charge be placed so net force on it is zero?
At the midpoint. By symmetry, two equal charges exert equal and opposite forces on any charge placed exactly midway. This works for ANY value of third charge (positive or negative)!
Q1 ★
The field E on the axial line of a dipole at distance r is 3.6×10⁵ N/C. What is E at the same distance on the equatorial line?
E_equatorial = E_axial/2 = 3.6×10⁵/2 = 1.8×10⁵ N/C. Use the golden rule: E_axial = 2×E_equatorial (when r >> a). Direction is OPPOSITE to dipole moment p.
Q2
The flux through a spherical surface of radius 5cm enclosing a charge is Φ. What is flux if radius is doubled to 10cm?
Still Φ! Gauss's law: Φ = q_enclosed/ε₀. Flux depends ONLY on enclosed charge, NOT on surface size. This is the most common NEET Gauss's law trap question!
Q3
A dipole in a uniform E makes 30° angle. Torque = 0.01 N·m. Find potential energy of the dipole.
τ = pE sin30° = 0.01 → pE = 0.02 N·m. U = −pE cos30° = −0.02 × (√3/2) = −0.0173 J ≈ −0.017 J. Negative PE indicates a configuration tending toward stability.
Q4
What is the work done in rotating a dipole by 180° from its stable equilibrium position in a field E?
W = U_final − U_initial = −pEcos(180°) − (−pEcos0°) = pE + pE = 2pE. Stable equilibrium is at θ=0°, unstable at θ=180°. Work done against field = 2pE.
Q5
Charges +q and +q are at (−a,0) and (+a,0). A charge +Q is at origin. What is the force on Q?
Zero! The two +q charges exert equal forces in OPPOSITE directions on Q at the origin. Net force = 0. This is unstable equilibrium — if Q displaces along y-axis, it escapes.
Q6
A charge Q is placed at the centre of a cube of side a. What is the electric flux through one face?
Total flux = Q/ε₀. Cube has 6 identical faces, all symmetric. Flux per face = Q/(6ε₀). Common mistake: students forget to divide by 6!
Q7
An infinite plane sheet has σ = 2×10⁻⁶ C/m². Find E on each side and between two oppositely charged parallel sheets.
Single sheet: E = σ/(2ε₀) = 2×10⁻⁶/(2×8.85×10⁻¹²) ≈ 1.13×10⁵ N/C on each side. Between two opposite sheets: fields ADD up, so E = σ/ε₀. Outside: fields cancel, E = 0.
Q8
Coulomb's law gives force F between charges in vacuum. How does force change if: (a) r is halved, (b) one charge is doubled, (c) medium of εᵣ = 3 is inserted?
(a) r halved → r² becomes r²/4 → F becomes 4F (quadruples). (b) q doubled → F becomes 2F (doubles). (c) εᵣ = 3 → F becomes F/3 (reduces to one-third). Each effect is independent by superposition.
Q9
Can the net electric force on a charge in a system of charges be zero even if the electric field is NOT zero?
No! F = qE. If E ≠ 0 and charge q ≠ 0, then force F = qE ≠ 0. The only way F = 0 on a non-zero charge is if E = 0 at that point. This is a conceptual trap question!
Q10
(NEET-type) Three charges +q, +q, −q are placed at vertices of an equilateral triangle of side a. Find the net force on −q.
Force from each +q on −q has magnitude F = kq²/a² (attractive, toward each +q). The two forces make 60° angle. Net = √(F²+F²+2F²cos60°) = F√3 = (√3·kq²)/a². Direction: toward midpoint of +q,+q side (by symmetry).
10

Common Mistakes

🚫 Force vs Field Confusion
❌ "Electric field is the force on a charge"
✓ E = F/q — field is force per unit charge. E exists even with no test charge present!
Fix: Always ask "force on what?" before writing the formula.
🚫 Gauss's Law Trap
❌ "Bigger Gaussian surface = more flux"
✓ Φ = q_enclosed/ε₀ — flux depends ONLY on enclosed charge, not surface size or shape
Fix: Draw the Gaussian surface and ONLY count charges inside it.
🚫 Dipole Moment Direction
❌ "Dipole moment points from + to −"
✓ p points from −q to +q (negative to positive). Opposite to the field direction between plates!
Fix: Remember "p points to positive" as a mnemonic.
🚫 Field Inside Conductor
❌ "E inside a charged conducting sphere = kQ/r²"
✓ E = 0 ALWAYS inside a conductor in electrostatic equilibrium. No exceptions!
Fix: Remember "conductor = E zero inside" as absolute rule.
🚫 Inverse Square Mistake
❌ "Double the distance → force halves"
✓ F ∝ 1/r² → Double distance → Force becomes ¼ (not ½!)
Fix: Write "r²" three times before doing any calculation.
🚫 Field Lines Form Loops
❌ "Electric field lines form closed loops"
✓ Only MAGNETIC field lines are closed loops. Electric field lines start on + and end on −.
Fix: Electric = open lines. Magnetic = closed loops. Never mix these up!
🚫 Superposition Scalar Sum
❌ Adding force magnitudes directly without considering directions
✓ Forces are vectors — resolve into x, y components, add algebraically, then find resultant magnitude
Fix: Always draw the force diagram first. Never add magnitudes without checking if they're parallel.
🚫 Dipole Equilibrium
❌ "θ = 90° is stable equilibrium (max torque)"
✓ θ = 0° is STABLE (min PE). θ = 180° is UNSTABLE. θ = 90° gives max torque but is NOT equilibrium!
Fix: Stable = dipole aligned with field (θ=0°). Torque tries to bring it there.
11

Quick Revision Sheet

🔑 Key Concepts
Charge unit: Coulomb (C), e = 1.6×10⁻¹⁹ C
q = ne (quantization, n = integer only)
Total charge in isolated system = constant
Conductor: E inside = 0 (always)
Like charges repel, unlike attract
Field lines: never cross, ⊥ to conductor
Dipole p: direction is −q → +q
E_axial = 2 × E_equatorial (golden rule!)
Flux depends only on enclosed charge
Stable equilibrium: θ=0° (p parallel to E)
📐 Core Formulas
F = kq₁q₂/r²
k = 9×10⁹ N·m²/C²
E = kq/r² = F/q₀
p = q × 2a (C·m)
E_axial = 2kp/r³
E_equatorial = kp/r³
τ = pE sinθ
U = −pE cosθ
Φ = EA cosθ
∮E·dA = q/ε₀
⚡ Gauss Applications
Sphere outside: E = kQ/r²
Sphere inside: E = 0
Line charge: E = λ/2πε₀r
Plane sheet: E = σ/2ε₀
🧠 Memory Tricks
r doubles → F becomes ¼
Axial = 2 × Equatorial
Flux = only enclosed charge
E inside conductor = ZERO
12

NEET & CBSE Exam Strategy

NEET Focus Areas
Coulomb's law proportionality questions (r doubled → F = ?)
E_axial vs E_equatorial comparison at same distance
Gauss's law — flux through different surfaces enclosing same charge
Field line properties (conceptual MCQs — 2-3 per year)
Quantization — "Is this charge possible?" type questions
Superposition with 3 charges in geometry
Torque and PE of dipole in external field
CBSE Focus Areas
Derivation: Coulomb's law, E due to dipole on axial/equatorial
State and prove Gauss's law (3–5 mark question)
Gauss's law applications — spherical shell, line charge, sheet
Properties of field lines — write all 8 with explanations
Conductors and electrostatics — why E=0 inside
Numericals on Coulomb's law + superposition
Draw and interpret electric field line patterns
⏱️ 3-Day Revision Strategy
Day
1
Re-read formulas, solve Level 1 & 2 questions. Revise field line properties.
Day
2
Focus on Gauss's law + dipole. Solve 10 NEET MCQs. Review common mistakes.
Day
3
Read Revision Sheet only. Trust your preparation. No new topics.
⏱️ Time strategy during exam: 1 min per MCQ. Skip and return if stuck. Coulomb's law + basic field questions are fastest (30 sec each). Superposition with geometry needs a diagram — attempt last.

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