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Science Grade XII Physics

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Chapter 1: Electric Charges and Fields

Grade 12 Science | Chapter 1

Electric Charges and Fields

Electric charge is the source of all electrical effects. This chapter develops charge and its properties, Coulomb’s law, the electric field and field lines, the dipole, and Gauss’s law.

Core Concepts

Key Principles

Worked Examples

Practice Sets

Contents

Introduction: Electric Charge

Coulomb’s Law

The Electric Field

The Electric Dipole

Gauss’s Law

Applications of Gauss’s Law

Key Reasoning (Principles)

Worked Examples (10)

Practice Sets A to D

10.

Summary and Exam Quick-Check

1. Introduction: Electric Charge

Electric charge is a basic property of matter that gives rise to all electrical effects. There are two kinds, positive and negative: like charges repel and unlike charges attract. Charge has two key properties. It is quantised, meaning it comes only in whole multiples of a smallest unit, the charge on one electron, written e. It is also conserved, meaning the total charge in an isolated system never changes.

Core idea

Charge is quantised (q equals n times e) and conserved. The force between charges follows Coulomb’s law, and the influence of a charge on the space around it is described by the electric field.

2. Coulomb’s Law

The force between two point charges was measured by Coulomb. Coulomb’s law states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them, F equals k times q1 times q2 divided by r squared, where k is about 9 times 10 to the power 9 in SI units. The force acts along the line joining the charges, repulsive for like charges and attractive for unlike.

Diagram 1 – Coulomb’s Law

Two point charges separated by distance r with repulsive Coulomb forces

Fig 1. Two like charges repel with equal and opposite forces along the line joining them, weaker as r grows.

3. The Electric Field

A charge changes the space around it, and we describe this with the electric field, E. The field at a point is the force per unit positive charge placed there, E equals F divided by q, measured in newtons per coulomb. The field of a point charge is E equals k times q divided by r squared. We picture the field with field lines that point away from a positive charge and toward a negative one, closer together where the field is stronger.

Diagram 2 – Electric Field Lines

Field lines of a positive charge, a negative charge and a dipole

Fig 2. Field lines point away from a positive charge, toward a negative charge, and from plus to minus in a dipole.

4. The Electric Dipole

An electric dipole is a pair of equal and opposite charges, plus q and minus q, separated by a small distance. Its strength and direction are given by the dipole moment, p equals q times d, a vector pointing from the negative to the positive charge. In a uniform field a dipole feels no net force but a torque that turns it to line up with the field, which is the basis of how many molecules respond to fields.

5. Gauss’s Law

Electric flux measures how much field passes through a surface. Gauss’s law gives a powerful link between flux and charge: the total electric flux through any closed surface equals the charge enclosed divided by the constant epsilon-naught, flux equals q divided by epsilon-naught. It depends only on the charge inside, not on where that charge sits or on any charges outside the surface.

Diagram 3 – Gauss’s Law

A point charge inside a Gaussian surface with field lines crossing it

Fig 3. The total flux out of a closed surface depends only on the charge enclosed within it.

6. Applications of Gauss’s Law

Gauss’s law makes it easy to find the field where there is symmetry. For a uniformly charged sphere, the field outside is the same as if all the charge sat at the centre. For an infinite charged sheet, the field is uniform and equal to the surface charge density divided by twice epsilon-naught, pointing away on both sides. For a long charged wire, the field falls off as one over the distance. In each case the symmetry lets us use Gauss’s law directly.

7. Key Reasoning (Principles)

Principle 1: Charge is quantised and conserved

Charge exists only in whole multiples of the basic unit e, and the total charge of an isolated system stays the same, so charge can be moved but never created or destroyed.

Principle 2: The force follows an inverse square law

By Coulomb’s law the force falls off as the square of the distance, so doubling the separation cuts the force to a quarter, just as gravity does with mass.

Principle 3: Flux depends only on the enclosed charge

Gauss’s law shows the total flux through a closed surface is set entirely by the charge inside it, which makes finding fields easy whenever there is symmetry.

8. Worked Examples

Example 1

Q: State the two kinds of electric charge and how they interact.

▶ Show Solution

Positive and negative; like charges repel and unlike charges attract.

Answer: Positive and negative; like repel, unlike attract.

Example 2

Q: What does it mean that charge is quantised?

▶ Show Solution

Charge comes only in whole multiples of the basic unit e.

Answer: q equals n times e.

Example 3

Q: Write Coulomb’s law.

▶ Show Solution

F equals k times q1 times q2 divided by r squared.

Answer: F = k q1 q2 / r squared.

Example 4

Q: Two charges are moved twice as far apart. What happens to the force?

▶ Show Solution

Force goes as one over r squared, so it falls to one quarter.

Answer: It becomes one quarter.

Example 5

Q: Define the electric field at a point.

▶ Show Solution

The force per unit positive charge placed at that point, E equals F divided by q.

Answer: E = F / q.

Example 6

Q: In which direction do field lines point near a positive charge?

▶ Show Solution

Away from the positive charge.

Answer: Away from it.

Example 7

Q: What is the electric dipole moment?

▶ Show Solution

p equals q times d, pointing from the negative to the positive charge.

Answer: p = q d.

Example 8

Q: What does a dipole experience in a uniform field?

▶ Show Solution

No net force, but a torque that turns it to line up with the field.

Answer: A torque (no net force).

Example 9

Q: State Gauss’s law.

▶ Show Solution

The total flux through a closed surface equals the enclosed charge divided by epsilon-naught.

Answer: flux = q / epsilon-naught.

Example 10

Q: A charge of 2 microcoulomb is enclosed by a surface. By what does the flux change if the charge doubles?

▶ Show Solution

Flux is proportional to the enclosed charge.

Doubling the charge doubles the flux.

Answer: It doubles.

9. Practice Sets A to D

Set A – Multiple Choice (Basic)

1. Like charges: (a) attract (b) repel (c) do nothing (d) merge

2. Charge is measured in: (a) newton (b) coulomb (c) volt (d) joule

3. Coulomb’s force varies with distance as: (a) 1/r (b) 1/r squared (c) r (d) r squared

4. Electric field is force per unit: (a) mass (b) positive charge (c) area (d) length

5. Gauss’s law relates flux to the: (a) outside charge (b) enclosed charge (c) area only (d) field only

▶ Reveal Answers

1. (b) repel.

2. (b) coulomb.

3. (b) 1/r squared.

4. (b) positive charge.

5. (b) enclosed charge.

Set B – Short Answer (Understanding)

1. State the two properties of charge.

2. Write Coulomb’s law and name each symbol.

3. Define the electric field and give its unit.

4. What is an electric dipole and its moment?

5. State Gauss’s law in words.

▶ Reveal Answers

1. Charge is quantised (whole multiples of e) and conserved (total stays constant).

2. F equals k q1 q2 divided by r squared; F is force, q1 and q2 the charges, r the separation, k the constant.

3. The force per unit positive charge, E equals F divided by q, in newtons per coulomb.

4. A pair of equal and opposite charges a small distance apart; its moment is p equals q times d, from minus to plus.

5. The total flux through any closed surface equals the charge enclosed divided by epsilon-naught.

Set C – Application and Reasoning

1. Two charges are brought three times closer. How does the force change?

2. Why do field lines never cross?

3. Why does a dipole turn in a uniform field but not move off?

4. Why does flux not depend on charges outside the surface?

5. Why is the field of a charged sphere, from outside, like a point charge?

▶ Reveal Answers

1. The force grows by a factor of nine, since it goes as one over r squared.

2. Because the field has only one direction at each point, so two lines cannot meet there.

3. Because the equal and opposite forces on its two charges give a turning torque but cancel as a net force.

4. Because their field lines that enter the surface also leave it, so they add no net flux.

5. Because, by symmetry, Gauss’s law gives the same field as if all the charge were at the centre.

Set D – Higher Order (Challenge)

1. Explain why charge being quantised was a surprising discovery.

2. Compare Coulomb’s law with the law of gravitation.

3. Explain how field lines show both the direction and the strength of a field.

4. Explain why Gauss’s law makes symmetric problems easy.

5. A charge sits at the centre of a cube. What fraction of the flux passes through one face, and why?

▶ Reveal Answers

1. Because charge appears smooth in everyday life, yet it is built from countless tiny equal units of e, like grains making sand.

2. Both are inverse square laws between two bodies, but Coulomb’s law acts on charge and can attract or repel, while gravity acts on mass and only attracts.

3. The direction of a line gives the field direction, and lines drawn closer together show where the field is stronger.

4. When the field has symmetry, the flux can be written simply over a chosen surface, so the field is found at once from the enclosed charge.

5. One sixth, because by symmetry the total flux q divided by epsilon-naught is shared equally among the six identical faces.

Chapter Summary

Charge

Two kinds; quantised (n times e) and conserved.

Coulomb’s Law

F equals k q1 q2 divided by r squared; inverse square.

Electric Field

E equals F divided by q; lines from plus to minus.

Dipole

Equal and opposite charges; moment p equals q d; feels a torque.

Gauss’s Law

Flux equals enclosed charge divided by epsilon-naught.

Applications

Field of a sphere, sheet and wire by symmetry.

Quantity

Unit

Symbol

Coulomb constant k

9 times 10^9

N m^2 / C^2

Field unit

N / C

–

Flux

q / epsilon-naught

–

8-Point Exam Quick-Check

Charge is quantised (q equals n times e) and conserved.

Like charges repel; unlike charges attract.

Coulomb’s law: F equals k q1 q2 divided by r squared (inverse square).

Electric field E equals F divided by q, in newtons per coulomb.

Field lines point away from plus, toward minus, and never cross.

A dipole has moment p equals q d and feels a torque in a field.

Gauss’s law: flux equals enclosed charge divided by epsilon-naught.

Symmetry plus Gauss’s law gives the field of spheres, sheets and wires.

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Class 12 Physics Chapter 1: Electric Charges and Fields, Complete Notes and Practice

This revision guide follows the current NCERT Class 12 Physics syllabus and develops electric charges and fields, covering the properties of charge, Coulomb’s law and the inverse square force, the electric field and field lines, the electric dipole and its moment, and Gauss’s law with its applications to a charged sphere, sheet and wire, with three diagrams, ten worked examples and graded practice. Visit SchoolRevise.com to revise, practise and excel.