Is it correct to say: Using r in cm directly inside Coulomb's law (F = kq₁q₂/r²)?

Always convert distance to metres before substituting. cm → 10⁻² m.

Is it correct to say: Treating electric field as scalar and ignoring direction?

E is a vector. When adding fields from multiple charges use vector components (Ex, Ey).

Is it correct to say: Writing capacitors in series gives larger equivalent capacitance?

Series ⇒ smaller (like adding springs). Parallel ⇒ larger. Reciprocal rule for series only.

Is it correct to say: Forgetting negative sign in E = −dV/dr?

The minus sign is physical — E points from high to low potential.

Is it correct to say: Confusing surface charge density σ (C/m²) with linear λ (C/m) or volume ρ (C/m³)?

Read the problem: sheet ⇒ σ, wire/rod ⇒ λ, solid ball ⇒ ρ. Units decide.

Is it correct to say: Substituting q with sign inside Coulomb's law and expecting positive answer?

For force magnitude use |q₁q₂|. Sign only tells attractive vs repulsive.

Electric Charges and Fields / Electrostatic Potential and Capacitance

Coulomb's law, electric field, potential, capacitance — NCERT Class 12 Physics Ch 1 & 2

📐 16 formulas✏️ 3 examples🎯 5 practice⚖️ 8 marks🏫 CBSE📚 Class 12✓ 2025–26 syllabus

💡

Board Exam Tips

→Coulomb's law derivation + 3-mark numerical is asked almost every year.
→Nernst equation appears in Chemistry — do NOT confuse with electric field formulas here.
→Capacitor combinations (series/parallel) usually carry a 3-mark question.
→Draw field lines carefully — positive→outward, negative→inward. Marks deducted for arrow errors.
→Always write units next to numerical answers. 1-mark lost otherwise.

📊 Diagram

Parallel-plate capacitor connected to a battery

📐 Formulas(16)

Coulomb's Law★ Board fav

F = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r ^{2}} = k \frac{q _{1} q _{2}}{r ^{2}}

Symbol	Meaning
$F$	Electrostatic force (N)
$k$	Coulomb's constant = 9×10⁹ N·m²/C²
$ε_{0}$	Permittivity of free space = 8.85×10⁻¹² C²/(N·m²)
$q_{1}, q_{2}$	Point charges (C)
$r$	Distance between charges (m)

Electric Field of Point Charge★ Board fav

E = \frac{F}{q _{0}} = k \frac{Q}{r ^{2}} r^

Electric Potential of Point Charge

V = k \frac{Q}{r}

Relation between E and V

E = - \frac{d V}{d r}

Electric Dipole Moment

p = q \cdot 2 a

Symbol	Meaning
$p$	Dipole moment (C·m)
$2 a$	Distance between the two charges (m)

Field on Axial Line of Dipole★ Board fav

E_{a x ia l} = \frac{1}{4 π ε _{0}} \frac{2 p}{r ^{3}} (r ≫ a)

Field on Equatorial Line of Dipole

E_{e q} = \frac{1}{4 π ε _{0}} \frac{p}{r ^{3}} (r ≫ a)

Gauss's Law★ Board fav

\oint E \cdot d A = \frac{q _{e n c}}{ε _{0}}

Field of Infinite Line Charge

E = \frac{λ}{2 π ε _{0} r}

Field of Infinite Plane Sheet

E = \frac{σ}{2 ε _{0}}

Capacitance

C = \frac{Q}{V}

Parallel-Plate Capacitor★ Board fav

C = \frac{ε _{0} A}{d}

Symbol	Meaning
$A$	Plate area (m²)
$d$	Separation between plates (m)

With Dielectric

C = \frac{K ε _{0} A}{d}

Energy Stored in Capacitor

U = \frac{1}{2} C V^{2} = \frac{Q ^{2}}{2 C} = \frac{1}{2} Q V

Capacitors in Series

\frac{1}{C _{e q}} = \frac{1}{C _{1}} + \frac{1}{C _{2}} + \dots

Capacitors in Parallel

C_{e q} = C_{1} + C_{2} + \dots

✏️ Solved Examples

1Solved Exampleeasy4 steps

Two charges +4 µC and −3 µC are placed 0.3 m apart. Find the electrostatic force between them.

List given quantities in SI units

q_{1} = 4 \times 1 0^{- 6} C, q_{2} = 3 \times 1 0^{- 6} C, r = 0.3 m

2Solved Exampleboard4 steps

A parallel-plate capacitor has plate area 100 cm² and separation 1 mm. A dielectric of K = 5 fills the gap. Find (a) capacitance, (b) charge stored when connected to a 12 V battery.

Convert to SI units

A = 100 cm^{2} = 1 0^{- 2} m^{2}, d = 1 0^{- 3} m

3Solved ExampleHOTS5 steps

Three capacitors 2 µF, 3 µF, 6 µF are connected first in series, then in parallel across a 12 V source. Find total energy stored in each case.

Series combination: reciprocal sum

\frac{1}{C _{s}} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \frac{3 + 2 + 1}{6} = 1 \Rightarrow C_{s} = 1 μ F

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Using r in cm directly inside Coulomb's law (F = kq₁q₂/r²)
✓Always convert distance to metres before substituting. cm → 10⁻² m.
2
Treating electric field as scalar and ignoring direction
✓E is a vector. When adding fields from multiple charges use vector components (Ex, Ey).
3
Writing capacitors in series gives larger equivalent capacitance
✓Series ⇒ smaller (like adding springs). Parallel ⇒ larger. Reciprocal rule for series only.
4
Forgetting negative sign in E = −dV/dr
✓The minus sign is physical — E points from high to low potential.
5
Confusing surface charge density σ (C/m²) with linear λ (C/m) or volume ρ (C/m³)
✓Read the problem: sheet ⇒ σ, wire/rod ⇒ λ, solid ball ⇒ ρ. Units decide.
6
Substituting q with sign inside Coulomb's law and expecting positive answer
✓For force magnitude use |q₁q₂|. Sign only tells attractive vs repulsive.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
Two point charges of +2 µC and +2 µC are 10 cm apart. Find the force between them and its nature.
Q2
Calculate the capacitance of a parallel-plate capacitor with plates of area 200 cm² separated by 0.5 mm (vacuum between).
Q3
An electric dipole of moment 4×10⁻⁹ C·m is placed in a uniform electric field of 5×10⁴ N/C. Maximum torque on dipole?
$τ_{ma x} = pE$
Q4
Three capacitors 4 µF, 4 µF and 4 µF are connected in series. Equivalent capacitance?
Q5
The electric potential 20 cm from a point charge is 60 V. Find the charge.

📝 Notes

Electric Charges, Fields and Capacitance

Study of stationary electric charges and the forces, fields and energies they produce.

Two-chapter overview

CBSE Class 12 packs two NCERT chapters into this topic:

Chapter 1 — Electric Charges and Fields: Coulomb's law, electric field, dipole, Gauss's law and its applications.
Chapter 2 — Electrostatic Potential and Capacitance: potential, potential energy, capacitors, dielectrics, energy stored.

Key principles

Charge is quantised: every charge is an integer multiple of e = 1.6×10⁻¹⁹ C.
Charge is conserved: total charge in an isolated system is constant.
Superposition: field due to multiple charges = vector sum of individual fields.