⚡ CBSE · Class 12 · Physics · Chapter 1

Electric Charges
and Fields

Complete chapter resources for CBSE Class 12 Physics — topic breakdown, key formulas, Coulomb's law, Gauss's law, sample questions, previous year board questions, and instant AI question paper generation.

5Topics
6–8Board marks
8Sample questions
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Key Formulas — Chapter 1
  • Coulomb's law: F = k·q₁q₂ / r², k = 9×10⁹ N·m²/C²
  • Electric field: E = F / q₀ = kQ / r² (N/C)
  • Dipole moment: p = q × 2a (C·m)
  • Torque on dipole: τ = p × E = pE sin θ
  • Gauss's law: Φ = q_enc / ε₀
  • Electric flux: Φ = E · A · cos θ (N·m²/C)
Chapter Overview

What this chapter covers

Chapter 1 of CBSE Class 12 Physics introduces the concept of electric charge — its quantisation (q = ne), conservation, and additive nature. It establishes Coulomb's law, which gives the force between two point charges: F = kq₁q₂/r², and explains the principle of superposition for systems of multiple charges. The concept of electric field as force per unit positive test charge is built up from here, giving students the vector field picture that underlies all of electrostatics.

The chapter then develops the concept of the electric dipole — two equal and opposite charges separated by a small distance. Students derive the electric field on the axial and equatorial lines of a dipole and obtain the expression for torque experienced by a dipole placed in a uniform electric field (τ = pE sin θ). Electric field lines, their properties, and electric flux (Φ = E·A·cos θ) are introduced as geometric tools for visualising field behaviour.

The chapter concludes with Gauss's law (Φ = q_enc/ε₀), one of the cornerstones of electromagnetism. Students apply it to highly symmetric charge distributions — infinite line charge, infinite plane sheet, and uniformly charged spherical shell — to derive the electric field in each case without lengthy integration. Board questions consistently include derivation-based long answers from these applications.

Topics

What's inside Chapter 1

As per NCERT Class 12 Physics Part I (CBSE syllabus)

Topic 1
Electric Charge & Coulomb's Law
Properties of charge — quantisation, conservation, additivity. Coulomb's force law in free space and in a medium (ε_r). Principle of superposition for systems of multiple point charges.
Topic 2
Electric Field & Field Lines
Definition of electric field intensity E = F/q₀. Field due to a point charge. Electric field lines: properties, uniform vs non-uniform fields, field between parallel plates.
Topic 3
Electric Dipole
Dipole moment p = q×2a. Electric field on axial line (E = 2kp/r³) and equatorial line (E = kp/r³). Torque on a dipole in a uniform external field: τ = pE sin θ.
Topic 4
Electric Flux & Gauss's Law
Electric flux Φ = E·A·cos θ. Gauss's law: total flux through a closed surface equals q_enc/ε₀. Concept of a Gaussian surface and its choice for symmetric distributions.
Topic 5
Applications of Gauss's Law
Field due to an infinitely long straight wire (E = λ/2πε₀r), an infinite plane sheet of charge (E = σ/2ε₀), and a uniformly charged spherical shell (field inside = 0, outside = kQ/r²).
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Class 11 · Laws of Motion
Vector forces, Newton's third law — needed for Coulomb interaction problems
Class 11 · Gravitation
Inverse-square law structure directly mirrors Coulomb's law
Chapter 1 Electric
Charges &
Fields
Leads to
Ch 2 · Electrostatic Potential & Capacitance
Electric potential energy and capacitors build directly on E-field concepts
Ch 4 · Moving Charges & Magnetism
Lorentz force and Biot-Savart law extend the field framework to magnetic fields
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 12 Physics board papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Assertion-Reason 1 1–2 Coulomb's law ratio problems, nature of charge, Gauss's law statement
Very Short Answer 2 1 Electric field due to a point charge, dipole moment definition, flux calculation
Short Answer 3 1 Superposition of forces, torque on dipole, properties of field lines
Long Answer / Derivation 5 1 Gauss's law applications, dipole field derivation, electric field at axial/equatorial points
Total (approximate) 6–8 4–5 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 12 Physics Chapter 1. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
Two point charges +4 μC and −4 μC are placed 20 cm apart in air. What is the electric field at the midpoint between them? (a) Zero (b) 7.2 × 10⁶ N/C directed from +q to −q (c) 7.2 × 10⁶ N/C directed from −q to +q (d) 3.6 × 10⁶ N/C
Q2 Easy 2 marks Short Answer
State two properties of electric field lines. Why do electric field lines never cross each other?
Q3 Medium 2 marks Short Answer
An electric dipole with dipole moment p = 6 × 10⁻⁸ C·m is placed in a uniform electric field of magnitude E = 3 × 10⁴ N/C. Calculate the maximum torque that can act on the dipole.
Q4 Medium 3 marks Short Answer
Three equal point charges, each of magnitude q = 2 μC, are placed at the three corners of an equilateral triangle of side 30 cm. Find the net force on any one of the charges due to the other two.
Q5 Medium 3 marks Short Answer
Using Gauss's law, derive an expression for the electric field intensity at a point outside a uniformly charged thin spherical shell of radius R carrying total charge Q. Draw the relevant diagram and Gaussian surface.
Q6 Hard 5 marks Long Answer
Derive an expression for the electric field on the axial line of a short electric dipole at a distance r from the centre. Hence show that for a short dipole the axial field is twice the equatorial field at the same distance.
Q7 Hard 5 marks Long Answer
State and prove Gauss's law in electrostatics. Using it, obtain an expression for the electric field due to an infinitely long straight wire of linear charge density λ at a perpendicular distance r from the wire. Draw the Gaussian surface used.
Q8 Hard 4 marks Word Problem
A square flat surface of side 10 cm is placed in a uniform electric field of 200 N/C directed at an angle of 30° to the normal of the surface. (i) Calculate the electric flux through the surface. (ii) If the surface is re-oriented so the field is parallel to the surface, what is the flux? (iii) State the physical significance of zero flux in context of Gauss's law.
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 12 Physics board papers — Electric Charges and Fields chapter.

Board 20223 marks
Using Gauss's law, derive an expression for the electric field intensity due to a uniformly charged infinite plane sheet. Draw the Gaussian surface used in the derivation. (CBSE All India 2022)
Board 20232 marks
A charge q is placed at the centre of a cube of side l. What is the electric flux through each face of the cube? (CBSE Delhi 2023)
Board 20205 marks
Define electric dipole moment. Derive an expression for the electric field at a point on the equatorial line of an electric dipole. Show that for a short dipole this field is directed opposite to the dipole moment vector. (CBSE 2020)
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FAQ

Questions teachers ask

How many marks does Electric Charges and Fields carry in the CBSE Class 12 Physics board exam? +
This chapter typically carries 6–8 marks in the CBSE Class 12 Physics board exam. Questions appear as a 1-mark MCQ on Coulomb's law or Gauss's law, a 2-mark short answer on electric field intensity or field lines, and a 3–5 mark long answer involving derivations such as the field due to a dipole or application of Gauss's law to symmetric charge distributions.
Which derivations from this chapter are most important for the CBSE board exam? +
The most frequently asked derivations are: (1) electric field on the axial and equatorial line of a dipole, (2) torque on a dipole in a uniform electric field, and (3) Gauss's law applied to a uniformly charged infinite plane sheet, a line charge, and a spherical shell. These appear almost every year and should be prepared in step-by-step format with diagrams.
What is the difference between electric field intensity and electric flux? +
Electric field intensity (E) is a vector quantity that describes the force experienced per unit positive test charge at a point in space, measured in N/C or V/m. Electric flux (Φ) is a scalar quantity representing the total number of electric field lines passing through a given surface area, calculated as Φ = E · A · cos θ, and measured in N·m²/C. Board questions frequently ask students to distinguish between these two quantities.
How is Gauss's law different from Coulomb's law, and when should each be used? +
Coulomb's law gives the force between two point charges directly: F = kq₁q₂/r². Gauss's law (Φ = q_enc/ε₀) relates the total electric flux through a closed surface to the net charge enclosed. Coulomb's law is convenient for point charges or simple geometries. Gauss's law is the powerful tool for finding E when the charge distribution has high symmetry — infinite plane, infinite line, or spherical shell — where choosing a suitable Gaussian surface simplifies the integral to E × A.
How do I generate a custom question paper for Electric Charges and Fields using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 12 Physics, select Chapter 1 (Electric Charges and Fields), set your preferred question-type mix (MCQ, short answer, word problem) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.