Electric Charges and Fields

part 1

Nature of Electric Charge

• Electric charges and their properties
• Conservation of charge
• Conductors and insulators
• Charging by induction

part 2

Coulomb's Law and Electric Field

• Coulomb's law — force between point charges
• Superposition principle
• Electric field concept and definition
• Electric field due to a point charge
• Electric field lines and their properties

part 3

Electric Dipole and Gauss Law

• Electric dipole and dipole moment
• Electric field due to a dipole
• Torque on a dipole in uniform electric field
• Electric flux
• Gauss's theorem and its applications
• Field due to infinite plane sheet and spherical shell

Coulomb's law

$F = \frac{kq_1 q_2}{r^2}$ (k = 9×10⁹ N m² C⁻²)

★ board favourite

Electric field due to point charge

$E = \frac{kq}{r^2}$ or $E = \frac{q}{4\pi\varepsilon_0 r^2}$

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Gauss's law

$\Phi_E = \oint \vec{E}\cdot d\vec{A} = \frac{q_{enc}}{\varepsilon_0}$

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Electric dipole moment

$p = q \times 2a$ (direction: −q to +q)

★ frequently asked

E on axial point of dipole

$E_{ax} = \frac{2kp}{r^3}$ (r >> a)

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E on equatorial point of dipole

$E_{eq} = \frac{kp}{r^3}$ (r >> a)

★ frequently asked

Torque on dipole in uniform field

$\tau = pE\sin\theta$ or $\tau = \vec{p} \times \vec{E}$

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E due to infinite line charge (λ)

$E = \frac{\lambda}{2\pi\varepsilon_0 r}$

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E due to infinite plane sheet (σ)

$E = \frac{\sigma}{2\varepsilon_0}$

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Electric flux

$\Phi = \vec{E}\cdot\vec{A} = EA\cos\theta$

★ frequently asked

Using Gauss's law, derive an expression for the electric field due to a uniformly charged infinite plane sheet. Two large parallel plane sheets have uniform surface charge densities +σ and −σ. Find the electric field in the region (i) between the sheets and (ii) outside the sheets.

An electric dipole of dipole moment p is placed in a uniform electric field E. Derive an expression for the torque acting on it and state the condition when the torque is (i) maximum and (ii) zero.

Two point charges +q and −q are placed at a distance d apart. What is the direction of the net electric field at the midpoint of the line joining them?

A charge q is placed at the centre of a cube of side a. What is the electric flux passing through each face of the cube? What happens to the flux if the charge is moved to a corner of the cube?

State Gauss's Law in electrostatics. Using it, derive the expression for electric field due to an infinitely long straight uniformly charged wire.

Using Gauss's law, derive an expression for the electric field at a point due to a uniformly charged thin spherical shell for points (i) outside, (ii) on, and (iii) inside the shell. Draw a graph of E versus r.

Define electric flux. A charge q is enclosed in a cube of side a. What is the electric flux through one face of the cube? Also state two properties of electric field lines.

Derive an expression for the electric field at a point on the equatorial line of an electric dipole. How does it compare with the axial field at the same distance?

The force between two point charges kept at a distance d apart in air is F. If the same charges are kept in a medium of dielectric constant K at the same distance, what is the new force?

Two identical metallic spheres carrying charges +6q and −2q are kept in contact and then separated to their original distance. Find the ratio of the force between them before and after contact.

Define electric dipole moment. Derive an expression for the electric field at a point on the axial line of an electric dipole.

Why do two electric field lines never intersect each other?

Define electric flux and write its SI unit. Using Gauss's law, obtain the expression for the electric field due to a long straight uniformly charged wire of linear charge density λ.

How many marks is Electric Charges and Fields worth in the Class 12 board exam?

Around 5 marks of the 70-mark CBSE Physics theory paper, based on the official unit-wise weightage. Master Gauss's Law applications — standard 3-mark questions.

Is Electric Charges and Fields easy or hard?

It's rated medium — a moderate-difficulty chapter in Class 12 Physics. Most students need about 4 hours to cover it well.

What are the important topics in Electric Charges and Fields?

The chapter covers 12 NCERT topics in 3 areas: Nature of Electric Charge; Coulomb's Law and Electric Field; Electric Dipole and Gauss Law.

What questions come from Electric Charges and Fields in board exams?

Between 2018–2024, CBSE board papers asked questions from this chapter on Gauss's Law, Electric Dipole, Coulomb's Law, Electric Flux — 1- to 5-mark questions.