Magnetism and Matter – Class 12 Physics

1. Introduction to Magnetism

Magnetism is a fundamental physical phenomenon exhibited by certain materials due to the motion of electric charges and the intrinsic magnetic properties of elementary particles. Long before the formal development of physics, humans observed that some naturally occurring stones could attract pieces of iron. These stones were later identified as natural magnets.

In modern physics, magnetism is understood as an essential aspect of electromagnetism, one of the four fundamental interactions of nature. This chapter develops a systematic and scientific understanding of magnetism strictly according to the NCERT Class 12 Physics syllabus, beginning from basic physical ideas and progressing towards the magnetic behaviour of materials.

[🖼️ DIAGRAM: Naturally occurring magnet (lodestone) attracting iron pieces, showing magnetic interaction without contact]

2. Magnetic Field

The concept of a magnetic field is introduced to describe magnetic interactions in space. A magnetic field is defined as the region surrounding a magnet or a current-carrying conductor in which magnetic effects can be detected.

If a magnetic material, another magnet, or a moving electric charge is placed within this region, it experiences a magnetic force. Thus, the magnetic field provides a physical means to represent magnetic influence.

The magnetic field is a vector quantity and is represented by the vector symbol 𝐁⃗. The SI unit of magnetic field is the tesla (T).

[🖼️ DIAGRAM: Region around a bar magnet indicating magnetic field at different points using arrows]

3. Magnetic Field Lines

Magnetic field lines are imaginary curves used to represent the magnetic field visually. They provide a convenient method to understand the spatial distribution and directional nature of the magnetic field.

The following properties describe magnetic field lines:

• The tangent to a magnetic field line at any point gives the direction of the magnetic field 𝐁⃗ at that point.
• Magnetic field lines form continuous closed loops.
• Outside a magnet, field lines emerge from the north pole and enter the south pole.
• The closeness of field lines indicates the strength of the magnetic field.

[🖼️ DIAGRAM: Closed magnetic field lines around a bar magnet with north and south poles clearly marked]

4. Bar Magnet as an Equivalent Solenoid

A bar magnet can be conceptually treated as equivalent to a solenoid carrying an electric current. Experimental observations show that the magnetic field pattern around a bar magnet closely resembles that of a long current-carrying solenoid.

Inside a long solenoid, the magnetic field is nearly uniform and parallel to its axis. Similarly, inside a bar magnet, the magnetic field lines are parallel and closely spaced.

[🖼️ DIAGRAM: Side-by-side comparison of magnetic field lines of a bar magnet and a current-carrying solenoid]

Where:
μ₀ = permeability of free space
n = number of turns per unit length of the solenoid
I = current through the solenoid

This equivalence establishes a deep connection between magnetism and electric currents and forms the basis of electromagnetic theory.

5. Magnetic Dipole and Magnetic Dipole Moment

A magnetic dipole consists of two equal and opposite magnetic poles separated by a small distance. A bar magnet represents a simple magnetic dipole.

The magnetic strength of a dipole is quantified by a vector quantity known as the magnetic dipole moment, denoted by 𝐌⃗.

[🖼️ DIAGRAM: Magnetic dipole showing north pole, south pole, separation 2l, and direction of magnetic dipole moment from south to north]

Where:
m = magnetic pole strength
2l = distance between the two poles

6. Magnetic Field Due to a Bar Magnet

The magnetic field produced by a bar magnet varies from point to point in space. To study this variation systematically, two special positions are considered: points lying on the axial line and points lying on the equatorial line of the magnet.

The analysis is carried out under the condition that the observation point is far away from the magnet compared to the separation of its poles.

[🖼️ DIAGRAM: Bar magnet showing axial line and equatorial line with observation point at distance r (r ≫ l)]

6.1 Magnetic Field on the Axial Line

The axial line of a bar magnet is the imaginary straight line passing through the centres of its north and south poles. Consider a point on this line at a distance r from the centre of the magnet.

[🖼️ DIAGRAM: Axial field geometry showing north and south poles and distances (r − l) and (r + l)]

Magnetic field due to south pole acts in the opposite direction:

The resultant magnetic field is obtained by subtracting these two contributions. Under the condition r ≫ l, the expression simplifies to:

where M = m × 2l is the magnetic dipole moment.

6.2 Magnetic Field on the Equatorial Line

The equatorial line of a bar magnet is the imaginary line passing through the centre of the magnet and perpendicular to its axis.

[🖼️ DIAGRAM: Equatorial field geometry showing perpendicular distances from poles]

At a point on the equatorial line, the horizontal components of the magnetic fields due to the two poles cancel each other, while the vertical components add up.

7. Magnetisation and Magnetic Intensity

When a magnetic material is placed in an external magnetic field, it becomes magnetised. This induced magnetic behaviour is described using two important quantities: magnetisation and magnetic intensity.

[🖼️ DIAGRAM: Magnetic material placed in external field showing alignment of atomic magnetic moments]

7.1 Magnetisation

Magnetisation is defined as the magnetic dipole moment per unit volume of the material.

7.2 Magnetic Intensity

Magnetic intensity, denoted by 𝐇⃗, represents the external magnetic field applied to a material. It depends only on the free currents producing the field and not on the nature of the material.

8. Magnetic Properties of Materials

The response of a material to an applied magnetic field depends on its internal structure. On this basis, materials are classified into three main categories.

[🖼️ DIAGRAM: Comparison of diamagnetic, paramagnetic and ferromagnetic materials in an external field]

8.1 Diamagnetic Materials

Diamagnetic substances are weakly repelled by a magnetic field. Their magnetic susceptibility is small and negative.

8.2 Paramagnetic Materials

Paramagnetic substances are weakly attracted by a magnetic field due to the presence of unpaired electrons.

8.3 Ferromagnetic Materials

Ferromagnetic substances show strong attraction and can retain magnetism even after the external field is removed.

[🖼️ DIAGRAM: Magnetic domains in ferromagnetic material showing domain alignment]

9. Earth as a Magnet

The Earth behaves like a giant magnet, producing a magnetic field that extends far into space. This field plays a crucial role in navigation and in protecting the Earth from charged particles of solar wind.

[🖼️ DIAGRAM: Earth’s magnetic field showing magnetic axis, geographic axis, north and south magnetic poles]

10. Solved Numerical Problems

Solved numerical problems are essential for understanding the quantitative application of magnetic concepts. The following problems are strictly based on the NCERT syllabus and examination pattern.

Problem 1: Magnetic Dipole Moment of a Bar Magnet

Given:
Magnetic pole strength, m = 0.4 A·m
Distance between poles, 2l = 8 cm = 0.08 m

To Find:
Magnetic dipole moment (M)

Formula Used:

Solution:
M = 0.4 × 0.08 = 0.032 A·m²

Answer:
The magnetic dipole moment of the bar magnet is 0.032 A·m².

Problem 2: Magnetic Field on the Axial Line

Given:
Magnetic dipole moment, M = 1.5 A·m²
Distance from centre, r = 20 cm = 0.2 m
μ₀ = 4π × 10⁻⁷ T·m/A

To Find:
Magnetic field on the axial line (B_axial)

Formula Used:

Solution:
B_axial = (10⁻⁷) × (2 × 1.5 / 0.2³)
B_axial = 3.75 × 10⁻⁵ T

Answer:
The magnetic field on the axial line is 3.75 × 10⁻⁵ T.

Problem 3: Magnetic Field on the Equatorial Line

Given:
Magnetic dipole moment, M = 0.8 A·m²
Distance, r = 0.1 m

To Find:
Magnetic field on the equatorial line (B_equatorial)

Formula Used:

Solution:
B_equatorial = 10⁻⁷ × (0.8 / 0.1³)
B_equatorial = 8 × 10⁻⁵ T

Answer:
The magnetic field on the equatorial line is 8 × 10⁻⁵ T.

Problem 4: Magnetic Field Inside a Solenoid

Given:
Number of turns per unit length, n = 1000 m⁻¹
Current, I = 2 A

To Find:
Magnetic field inside the solenoid (B)

Solution:
B = 4π × 10⁻⁷ × 1000 × 2
B = 2.51 × 10⁻³ T

Answer:
The magnetic field inside the solenoid is 2.51 × 10⁻³ T.

11. Applications of Magnetism

Magnetism plays a vital role in natural phenomena as well as in modern technology. Some important applications are listed below.

• Electric motors and generators operate on magnetic principles.
• Magnetic compasses use Earth’s magnetic field for navigation.
• Data storage devices such as hard disks rely on ferromagnetic materials.
• Transformers and inductors are based on magnetic fields.
• Magnetic resonance imaging (MRI) uses strong magnetic fields for medical diagnosis.

12. Summary and Points to Remember

• Magnetism arises due to moving electric charges.
• A bar magnet behaves like a magnetic dipole.
• Magnetic field decreases inversely with the cube of distance.
• Materials respond differently to external magnetic fields.
• Earth itself behaves like a giant magnet.

13. Multiple Choice Questions (MCQs)

1. The SI unit of magnetic field is:
   Answer: Tesla (T) — It measures magnetic flux density.
2. Magnetic field lines:
   Answer: Form closed continuous loops.
3. The direction of magnetic dipole moment is from:
   Answer: South pole to North pole.
4. The magnetic field on the axial line of a dipole varies as:
   Answer: 1/r³ — Dipole field decreases rapidly with distance.
5. Which material has large positive magnetic susceptibility?
   Answer: Ferromagnetic material.
6. The magnetic field inside a long solenoid is:
   Answer: Uniform and parallel to its axis.
7. Which quantity depends only on free currents?
   Answer: Magnetic intensity (H).
8. Diamagnetic materials are:
   Answer: Weakly repelled by magnetic field.
9. The Earth’s magnetic field resembles that of:
   Answer: A bar magnet.
10. Magnetic field on equatorial line is:
    Answer: Half of axial field at same distance.

(For examination brevity, remaining MCQs follow the same NCERT-aligned pattern up to 50 questions.)

14. Very Short Answer Questions (VSA)

1. Define magnetic dipole moment.
2. State the SI unit of magnetic field.
3. What is magnetisation?
4. What type of material is copper?
5. Name the magnetic elements of Earth.
6. What is a magnetic field line?
7. State one use of a solenoid.
8. What is permeability of free space?
9. Define magnetic intensity.
10. What is ferromagnetism?

15. Short Answer Questions (SA)

1. Explain the concept of magnetic field.
2. Describe properties of magnetic field lines.
3. Why are magnetic monopoles not observed?
4. Explain the equivalence of bar magnet and solenoid.
5. Define magnetisation and magnetic intensity.
6. Differentiate between dia- and paramagnetic substances.
7. Explain the domain theory of ferromagnetism.
8. Derive expression for axial magnetic field of a bar magnet.
9. What causes Earth’s magnetic field?
10. Explain the importance of Earth’s magnetic field.

16. Long Answer Questions (LA)

1. Derive expressions for magnetic field due to a bar magnet on axial and equatorial lines.
2. Explain magnetic properties of materials with examples.
3. Describe magnetisation and derive relation between B, H and M.
4. Explain Earth as a magnet and define magnetic elements.
5. Describe bar magnet as an equivalent solenoid.

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