Electrostatics — Class 12 / NEET / JEE
CBSE Class 12 Physics

Electrostatics
Made Simple

Unit I · Electric Charges & Fields + Electrostatic Potential & Capacitance
Designed for NEET / JEE aspirants with weak fundamentals

Step-by-step concepts Real-life analogies Interactive MCQs Formula sheet
Charge
Coulomb
E-Field
Gauss
Potential
Capacitance
Core Concepts
Build from zero — step by step, no shortcuts skipped
01
Foundation
What is Electric Charge?
Electric charge is a fundamental property of matter — just like mass. You can't see it, but you feel its effects every day. When you rub a plastic comb on dry hair, the comb picks up tiny paper bits. Why? Rubbing causes transfer of tiny invisible particles called electrons, giving the comb a charge.
Real life: Balloon rubbed on hair → sticks to wall. Lightning in storms. Static shock when touching metal in winter. All caused by electric charges!
Two types of charge:

🔴 Positive (+) — protons carry this. Example: glass rod rubbed with silk.
🔵 Negative (−) — electrons carry this. Example: plastic rod rubbed with wool.

Golden Rule: Like charges REPEL. Unlike charges ATTRACT.
(Like is boring — they push away. Unlike is exciting — they pull together!)
02
Properties
Properties of Electric Charge
Conservation of Charge:
Charge is never created or destroyed — only transferred. Total charge in the universe is always constant. Before = After.

Quantization of Charge:
Charge comes in fixed, discrete packets. You cannot have half an electron. Every charge is a whole-number multiple of the smallest charge unit:
Quantization
q = n × e   |   e = 1.6 × 10⁻¹⁹ C
n = any integer (1, 2, 3...) — never a fraction
Think of charge like coins. You can have ₹1, ₹2, ₹5 — but never ₹1.37. Electrons are the "coins" of charge!
03
Force Between Charges
Coulomb's Law
Two charges placed near each other feel a force. Coulomb measured this exactly. The force depends on the size of both charges and the distance between them.
Coulomb's Law
F = k · q₁q₂ / r²
k = 9×10⁹ N·m²/C²  |  r = distance between charges (metres)
Key observations:
— More charge → more force
— Greater distance → MUCH less force (r² in denominator!)
— Double the distance → force becomes 4× weaker (Inverse Square Law)
— Same sign charges → F is repulsive
— Opposite sign charges → F is attractive
Two magnets: bring them closer → stronger force. Move apart → weaker force. Coulomb's law puts exact numbers on this behavior for electric charges.
Thinking moment: If charge q₁ is doubled AND distance is also doubled, by what factor does the force change? Try calculating before reading on!
04
Influence Zone
Electric Field & Field Lines
A charge creates an invisible region around itself where it can push or pull other charges. This region is the Electric Field. Even if no other charge is present, the field exists!
Electric Field
E = F / q     E = kQ / r²
E = field strength (N/C or V/m)  |  Q = source charge  |  r = distance from source
Electric Field Lines — visualize this:

— Lines shoot OUTWARD from positive charges (they're "escaping")
— Lines point INWARD into negative charges (they're "entering")
— Lines NEVER cross each other
— Crowded lines = STRONG field. Spread-out lines = weak field
— Always drawn with arrows showing direction
Critical difference: Force (F) needs TWO charges interacting. Electric field (E) is created by just ONE charge. F = qE connects them. Don't mix these up in MCQs!
05
Powerful Shortcut
Gauss's Law
Instead of adding forces from every charge one by one, Gauss's law gives us the total electric flux through any closed surface — using just the total enclosed charge. We use an imaginary closed surface called a Gaussian Surface.
Gauss's Law
Φ = Q_enclosed / ε₀
Φ = electric flux (N·m²/C)  |  ε₀ = 8.85×10⁻¹² C²/N·m²
Imagine a glowing bulb inside a balloon. The total light escaping through the balloon depends only on the brightness of the bulb — not on how big or what shape the balloon is. Same logic with Gauss's Law!
When to use Gauss's Law: Only when there is clear symmetry — spherical, cylindrical, or planar. For NEET, the most common application is finding field of uniformly charged sphere or infinite plane sheet.
06
Energy Landscape
Electric Potential & Potential Difference
Electric potential at a point is the work done to bring a unit positive charge from infinity to that point — slowly, without acceleration. It's a scalar (no direction!).
Electric Potential
V = kQ / r     V = W / q
V = potential (Volts)  |  W = work done (Joules)  |  q = charge moved
Think of potential like altitude on a hill. Water naturally flows downhill (high to low). Positive charges "flow" from high potential to low potential — just like water! This is why current flows in circuits.
Potential Difference: ΔV = V_A − V_B = W/q

This is what we call Voltage in daily life! The 230V at your socket = potential difference between the two terminals. It's what drives current through your devices.
V is a scalar — it has no direction. E is a vector. At the midpoint between two equal and opposite charges, V = 0 but E ≠ 0. This confuses many students in exams!
07
Charge Storage Device
Capacitance & Capacitors
A capacitor stores electric charge (and energy). It has two parallel conducting plates facing each other, separated by a gap or insulating material (dielectric). When connected to a battery, one plate gets +Q and the other −Q.
Capacitance & Parallel Plate Formula
C = Q / V     C = ε₀A / d     (with dielectric: C = κε₀A / d)
C = capacitance (Farads)  |  A = plate area  |  d = plate separation  |  κ = dielectric constant
Capacitor = Rechargeable water tank. Bigger tank (larger A), shallower tank (smaller d) → holds more water (charge) at the same water pressure (voltage). Adding dielectric is like using a special tank material that holds more!
Energy stored in capacitor:
U = ½CV² = ½QV = Q²/2C

Combinations:
Series: 1/C_total = 1/C₁ + 1/C₂ (total C decreases)
Parallel: C_total = C₁ + C₂ (total C increases)
Note: This is OPPOSITE to resistors!
📐
Formula Sheet
All key formulas with usage notes — exam-ready reference
Quantization of Charge
q = ne
n = integer  |  e = 1.6 × 10⁻¹⁹ C
Use when: finding charge for n electrons/protons
Coulomb's Law
F = kq₁q₂ / r²
k = 9×10⁹ N·m²/C²  |  r in metres
Use when: force between two point charges
Electric Field
E = F/q = kQ/r²
Unit: N/C or V/m
Use when: finding field at a distance r from charge Q
Gauss's Law
Φ = Q / ε₀
ε₀ = 8.85×10⁻¹² C²/N·m²
Use when: symmetric charge distributions
Electric Potential
V = kQ / r
Unit: Volt (V) = J/C
Use when: potential at distance r from charge Q
Potential Difference
ΔV = W / q
W = work done (Joules)
Use when: work done moving charge between two points
Capacitance
C = Q / V
Unit: Farad (F)
Use when: relating charge stored to voltage
Parallel Plate Capacitor
C = ε₀A / d
A = plate area  |  d = separation
Use when: finding capacitance from geometry
With Dielectric
C = κε₀A / d
κ = dielectric constant ≥ 1
Use when: insulating material fills the gap
Energy Stored
U = ½CV²
Also: U = Q²/2C = ½QV
Use when: energy in a charged capacitor
Capacitors in Series
1/C = 1/C₁ + 1/C₂
Total C is LESS than smallest C
Voltage divides, charge is same
Capacitors in Parallel
C = C₁ + C₂
Total C is MORE than largest C
Voltage is same, charge divides
⚠️ Key constants to memorize:   k = 9×10⁹ N·m²/C²  |  ε₀ = 8.85×10⁻¹² C²/N·m²  |  e = 1.6×10⁻¹⁹ C  |  Note: k = 1/(4πε₀). Always convert μC → 10⁻⁶ C and mm → 10⁻³ m before substituting!
🔢
Solved Examples
4-step method — identify, select, substitute, solve
Example 01 — Coulomb's Law
Two charges of +3 μC and −5 μC are placed 0.3 m apart in vacuum. Find the electrostatic force between them.
1
Given values
q₁ = +3 μC = 3×10⁻⁶ C  |  q₂ = −5 μC = 5×10⁻⁶ C  |  r = 0.3 m  |  k = 9×10⁹ N·m²/C²
2
Formula selected
F = k · q₁q₂ / r²
3
Substituting values
F = (9×10⁹ × 3×10⁻⁶ × 5×10⁻⁶) / (0.3)²
4
Solving step by step
Numerator = 9×10⁹ × 15×10⁻¹² = 135×10⁻³ = 0.135
Denominator = (0.3)² = 0.09
F = 0.135 / 0.09 = 1.5 N
✅ Answer: F = 1.5 N — Attractive force (opposite sign charges always attract)
Example 02 — Electric Potential
Find the electric potential at a point 0.5 m away from a charge of +2 μC in free space.
1
Given values
Q = +2 μC = 2×10⁻⁶ C  |  r = 0.5 m  |  k = 9×10⁹
2
Formula selected
V = kQ / r
3
Substituting values
V = (9×10⁹ × 2×10⁻⁶) / 0.5
4
Solving step by step
V = 18000 / 0.5 = 36,000 V = 36 kV
✅ Answer: V = 36,000 V = 36 kV (positive, since source charge is positive)
Example 03 — Capacitance
A parallel plate capacitor has plate area 0.02 m² and plate separation 2 mm. Find its capacitance in free space.
1
Given values
A = 0.02 m²  |  d = 2 mm = 2×10⁻³ m  |  ε₀ = 8.85×10⁻¹²
2
Formula selected
C = ε₀A / d
3
Substituting values
C = (8.85×10⁻¹² × 0.02) / (2×10⁻³)
4
Solving step by step
Numerator = 1.77×10⁻¹³  |  Denominator = 2×10⁻³
C = 1.77×10⁻¹³ / 2×10⁻³ = 8.85×10⁻¹¹ F
✅ Answer: C ≈ 88.5 pF (picofarads) — typical value for small capacitors
🎯
MCQ Practice
Click an option — instant feedback + explanation
Q 01 Easy
If the distance between two point charges is doubled, the electrostatic force between them becomes:
Correct: B — One-fourth
F = kq₁q₂/r². When r → 2r, the denominator becomes (2r)² = 4r². So F becomes F/4 = one-fourth. This is the Inverse Square Law. In exams, when distance is multiplied by n, force is divided by n². Common trap: students pick "half" thinking it's linear — it's not!
Q 02 Easy
Electric field lines around a single isolated positive charge:
Correct: B — Outward away from the charge
Field lines always START at positive charges and END at negative charges. A lone positive charge is a "source" — field lines radiate outward in all directions like a sunburst. Remember: positive = radiating out, negative = converging in. This appears in NEET every 2-3 years.
Q 03 Moderate
A capacitor of capacitance C is charged to potential V. The energy stored in it is:
Correct: C — ½CV²
U = ½CV². The ½ factor appears because voltage builds from 0 to V gradually during charging — so we use the average voltage (V/2). Option A (CV = Q) is charge, not energy. Trap: option B looks similar but missing the ½. Also remember: U = Q²/2C = ½QV are all equivalent forms.
Q 04 Moderate
Which statement about electric potential is correct?
Correct: B — Scalar quantity
V is a scalar — no direction. E is a vector. V depends only on source charge Q and distance r — NOT on any test charge. V = kQ/r, and if Q is negative, V is negative. V CAN be zero (midpoint between +Q and −Q). This distinction between V (scalar) and E (vector) is heavily tested!
Q 05 Moderate
A dielectric slab is inserted between the plates of an isolated charged capacitor (disconnected from battery). Which quantity increases?
Correct: A — Capacitance increases
Dielectric increases C (C = κε₀A/d, κ > 1 means C increases). Since capacitor is isolated (disconnected), Q stays constant. With Q fixed and C increased: V = Q/C → V decreases. E = V/d → E also decreases. So only C increases! Classic NEET trap: always check if battery is connected or disconnected — changes everything!
⚠️
Common Mistakes
Avoid these — they cost marks in every exam
🔀
Confusing E and F
Students write E = kq₁q₂/r² (wrong!) or use force formula when field is asked.
F needs two charges (F = kq₁q₂/r²). E is from one charge (E = kQ/r²). They're connected by F = qE.
➕➖
Ignoring sign of charges
Treating all charges as positive in force problems, getting wrong direction.
Always check: same sign → repulsion, opposite sign → attraction. Sign matters for direction, not magnitude formula.
📏
Forgetting unit conversion
Using μC directly as C, or cm as m in formulas — giving answers off by factors of 10⁶.
Always convert: 1 μC = 10⁻⁶ C, 1 mm = 10⁻³ m, 1 cm = 10⁻² m. Do this BEFORE substituting.
🔮
Wrong Gauss's Law application
Using Gauss's law for non-symmetric charge distributions where it doesn't simplify.
Gauss's law is always true, but only useful with symmetry: spherical, cylindrical, or planar. No symmetry → use Coulomb's law instead.
🎭
V = 0 means E = 0
Assuming zero potential means zero field — wrong! Midpoint of dipole has V = 0 but E ≠ 0.
V and E are related by E = −dV/dr. V = 0 just means net work done is zero. Field can still exist.
🔋
Battery connected or not?
In capacitor problems, ignoring whether battery is connected changes which quantity stays constant.
Battery connected → V is constant, Q changes. Battery disconnected (isolated) → Q is constant, V changes. This determines everything else!
🚀
Quick Revision
Memory tricks, chapter summary & exam prep
🌟
PNRA Rule (Field Lines)
Positive = Radiating Away. Negative = Reaching Across. Field lines always travel from + to −. Never forget this direction!
🎭
V is Shy, E is Bold
V is scalar (no direction = shy). E is vector (has direction = bold). V can be 0 while E ≠ 0. They differ fundamentally in nature.
🪣
Bigger Tank = Bigger C
Large area A, small gap d, bigger κ → bigger capacitance. Like a wide, shallow water tank holding more water at same pressure.
➗✖️
Series Shrinks, Parallel Pumps
Capacitors in series → C decreases. In parallel → C increases. This is OPPOSITE to resistors! Don't mix them up in problems.
9️⃣
k = 9 × 10⁹ Always
Coulomb's constant k = 9×10⁹ N·m²/C². Never change this. It appears in F, E, and V formulas for point charges.
📐
Inverse Square Club
F ∝ 1/r² and E ∝ 1/r² (square of distance). But V ∝ 1/r (linear with distance). Distance doubles → F,E become ¼× but V becomes ½×.

Chapter at a Glance

Electric Charge
Two types (+, −) | Conserved | Quantized: q = ne | e = 1.6×10⁻¹⁹ C
Coulomb's Law
F = kq₁q₂/r² | k = 9×10⁹ | Inverse square law | Like repel, unlike attract
Electric Field
E = F/q = kQ/r² | Vector | Lines: out of +, into − | Never cross
Gauss's Law
Φ = Q/ε₀ | Use only with symmetry: spherical/cylindrical/planar
Electric Potential
V = kQ/r | Scalar | V = W/q | V can be negative | V≠0 when E=0 possible
Capacitance
C = Q/V = ε₀A/d | Unit: Farad | With dielectric: C = κε₀A/d (κ ≥ 1)
Energy in Capacitor
U = ½CV² = Q²/2C = ½QV | Series: 1/C = Σ(1/Cᵢ) | Parallel: C = ΣCᵢ
Electrostatics · CBSE Class 12 · NEET / JEE Preparation
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