1. Introduction to Magnetism | Class 12 Physics Chapter 5 Magnetism and Matter Notes

Welcome, students! Today we embark on a fascinating journey into the world of Magnetism and Matter. In our previous chapter, “Moving Charges and Magnetism,” we established a fundamental link: electric currents produce magnetic fields. This was the dawn of electromagnetism, credited to giants like Oersted and Ampere. However, today we step back to look at magnetism as a property inherent to matter itself, independent of wires and batteries.

The story of magnetism is not new. In fact, it predates human evolution. The very word “magnet” finds its origins in the name of an island in Greece called Magnesia. Historical records suggest that magnetic ore deposits were discovered there as early as 600 BC. Imagine shepherds in ancient Greece complaining that their wooden shoes—held together by iron nails—were mysteriously sticking to the ground! That was humanity’s first encounter with this invisible force.

In this chapter, we will treat magnetism as a subject in its own right. We will explore why the earth itself behaves like a giant magnet, why a compass needle always points North, and why you can never, ever find a “North Pole” all by itself. We will also categorize every material in the universe based on how it reacts to a magnet—whether it is water, copper, or iron. Let’s dive in.

2. The Bar Magnet and Its Properties

2.1 Fundamental Observations

A bar magnet is the most familiar object in this field. Before we get into the complex mathematics, let’s list the non-negotiable, fundamental rules of magnetic behavior that you must memorize:

• The Directional Property: If you take a bar magnet and suspend it freely by a thread, it will not hang randomly. It will rotate and eventually settle in a specific direction—the geographic North-South direction. The tip that points to the geographic North is defined as the North Pole, and the tip pointing South is the South Pole. This property was used by ancient navigators for centuries.
• Attractive and Repulsive Forces: This is the rule you learned in primary school. Like poles repel each other (North repels North, South repels South). Conversely, unlike poles attract each other (North attracts South).
• The Non-Existence of Monopoles: This is the most crucial conceptual difference between electricity and magnetism. In electrostatics, you can isolate a single positive charge (+q). In magnetism, isolated magnetic poles (monopoles) do not exist.
  
  Teacher’s Explanation: Imagine you have a bar magnet. You cut it in half to separate the North pole. What happens? You don’t get a separate “N” and “S”. You get two smaller, complete magnets, each with its own North and South pole. You can keep cutting it down to the atomic level, and even the atom acts as a dipole. Magnetic poles always come in pairs.
• Magnetic Materials: It is possible to manufacture magnets out of iron and its alloys. Not all metals are magnetic, but iron is the prime example we use.

2.2 Magnetic Field Lines

Just as we visualize the electric field using electric field lines, we visualize the magnetic field ($\mathbf{B}$) using magnetic field lines. We can see these physically by sprinkling iron filings on a glass sheet placed over a bar magnet. The filings align themselves in a specific pattern, forming curved chains that map out the magnetic field.

Figure-1: The arrangement of iron filings surrounding a bar magnet (a) and a current-carrying solenoid (b). Notice the striking similarity in their patterns.

Crucial Properties of Magnetic Field Lines (Board Exam Focus):

1. Continuous Closed Loops: This is the most important property. Magnetic field lines form continuous closed loops.
   
   Contrast with Electrostatics: Electric field lines start at a positive charge and end at a negative charge (or go to infinity). They are discontinuous.
   
   In Magnetism: Outside the magnet, lines move from North to South. But inside the magnet, they move from South to North to complete the loop. They have no beginning and no end.
2. Direction of Field: The tangent to the field line at any given point gives the direction of the net magnetic field ($\mathbf{B}$) at that point.
3. Field Strength Indicator: The density of the lines represents the strength of the field. The larger the number of field lines crossing per unit area, the stronger the magnitude of the magnetic field $\mathbf{B}$. This is why lines are crowded near the poles (strong field) and spread out far away (weak field).
4. No Intersections: Two magnetic field lines can never intersect.
   
   Reasoning: If they did intersect at a point P, you could draw two different tangents at that single point. This would mean the magnetic field has two different directions at the same instant, which is physically impossible.

3. The Solenoid Analogy

3.1 Why a Bar Magnet is essentially a Solenoid

In Chapter 4, we learned that a current-carrying solenoid behaves like a magnet. If we look at the magnetic field lines of a bar magnet and a finite solenoid, they are remarkably similar.

Teacher’s Insight: We can think of a bar magnet as a collection of circulating currents on the atomic scale, just like a solenoid is a collection of circulating currents in a wire. Cutting a magnet is like cutting a solenoid—you just get smaller solenoids with weaker properties, but the basic structure remains.

3.2 Mathematical Proof (Axial Field)

We can verify this analogy mathematically. Consider a finite solenoid. We can demonstrate that at large distances, the axial field of a solenoid is identical to that of a bar magnet.

The magnetic field $B$ at a large distance $r$ from the center of a solenoid (or bar magnet) on its axis is given by Eq. (5.1):

$$B = \frac{\mu_{0}}{4\pi} \frac{2m}{r^{3}}$$

Here, $m$ is the Magnetic Dipole Moment.

For a bar magnet, $m$ is its inherent strength.

For a solenoid with $N$ turns, current $I$, and cross-sectional area $A$, the magnetic moment is calculated as $m = N I A$.

This equation confirms that a bar magnet and a solenoid produce similar magnetic fields at large distances.

4. The Dipole in a Uniform Magnetic Field

What happens when we place a small bar magnet (or a compass needle) with magnetic moment $\mathbf{m}$ in a uniform external magnetic field $\mathbf{B}$?

Since the field is uniform, the North pole experiences a force $\mathbf{F}$ in the direction of the field, and the South pole experiences a force $-\mathbf{F}$ opposite to the field.

Net Force: The total force on the dipole is zero.

Torque: However, these two equal and opposite forces act at different points, forming a couple. This creates a torque $\tau$ that tries to rotate the magnet.

4.1 Torque Calculation

The torque $\boldsymbol{\tau}$ is given by the vector product:
$$\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}$$
In magnitude, this is written as:
$$\tau = m B \sin \theta$$
where $\theta$ is the angle between the magnetic moment $\mathbf{m}$ and the magnetic field $\mathbf{B}$.

4.2 Potential Energy ($U_m$)

As the magnet rotates, work is done against the restoring torque. This work is stored as potential energy in the system.

The magnetic potential energy $U_m$ is derived by integrating the torque:
$$U_m = \int \tau(\theta) d\theta = \int mB \sin \theta d\theta$$
$$U_m = -mB \cos \theta$$
In vector notation:
$$U_m = -\mathbf{m} \cdot \mathbf{B}$$

Figure-2: The potential energy of a dipole varies with its orientation in the magnetic field.

4.3 Equilibrium Cases (Important for VIVA)

We take the zero of potential energy at $\theta = 90^\circ$. Based on this:

• Stable Equilibrium ($\theta = 0^\circ$): The magnetic moment $\mathbf{m}$ is parallel to the field $\mathbf{B}$.
  
  Energy $U = -mB \cos(0^\circ) = -mB$.
  
  This is the minimum energy state. The magnet is most stable here.
• Unstable Equilibrium ($\theta = 180^\circ$): The magnetic moment $\mathbf{m}$ is anti-parallel to the field $\mathbf{B}$.
  
  Energy $U = -mB \cos(180^\circ) = +mB$.
  
  This is the maximum energy state. Even a tiny disturbance will cause the magnet to flip over.
• Zero Energy ($\theta = 90^\circ$): When the magnet is perpendicular to the field, $U = 0$. This is our reference point.

5. The Electrostatic Analog

Physics is beautiful because patterns repeat. You do not need to memorize a new set of formulas for Magnetism if you remember Chapter 1 (Electrostatics). The equations are identical in form, with specific replacements.

The Substitution Rule:

• Replace Electric Field $\mathbf{E}$ with Magnetic Field $\mathbf{B}$.
• Replace Electric Dipole Moment $\mathbf{p}$ with Magnetic Dipole Moment $\mathbf{m}$.
• Replace the constant $\frac{1}{4\pi\epsilon_0}$ with $\frac{\mu_0}{4\pi}$.

Note: The axial field is twice as strong as the equatorial field for the same distance $r$ (provided $r$ is much larger than the magnet size).

6. Gauss’s Law for Magnetism

In electrostatics, Gauss’s law ($\oint \mathbf{E} \cdot d\mathbf{S} = q/\epsilon_0$) tells us that the net flux depends on the enclosed charge. Flux lines can start from a positive charge and leave the surface.

In magnetism, the situation is radically different because isolated magnetic poles do not exist. There are no “sources” (monopoles) from which magnetic field lines emanate outward to infinity.

The Statement:
The net magnetic flux through any closed surface is always zero.

$$\oint \mathbf{B} \cdot d\mathbf{S} = 0$$

Physical Interpretation:
Consider any closed surface (like a box or a sphere) in a magnetic field. The number of magnetic field lines entering the surface must exactly equal the number of field lines leaving it. You cannot “trap” a net amount of magnetic flux inside a box because the lines are continuous loops—if a line enters, it must exit.

This law is the mathematical verification that magnetic monopoles do not exist.

7. Magnetization and Magnetic Intensity

When we place a bulk material in an external magnetic field, it responds. The atoms inside align or induce currents. To quantify this, we define specific terms. Be careful not to mix them up!

7.1 Definitions

• Magnetization ($\mathbf{M}$):
  This measures how perfectly the material is magnetized. It is defined as the net magnetic dipole moment per unit volume.
  $$M = \frac{m_{net}}{V}$$
  Unit: Amperes per meter ($A m^{-1}$).
  
  Dimensions: $[L^{-1} A]$.
• Magnetic Intensity ($\mathbf{H}$):
  This vector represents the external magnetizing field (e.g., the field produced by the free current in a solenoid) without the material’s contribution. It is defined as:
  $$H = \frac{B}{\mu_0} – M$$
  Unit: Amperes per meter ($A m^{-1}$).
• Magnetic Susceptibility ($\chi$):
  This is a dimensionless quantity that tells us how “responsive” a material is to the external field. It relates $M$ and $H$:
  $$M = \chi H$$
  If $\chi$ is positive, the material is attracted (Paramagnetic). If $\chi$ is negative, it is repelled (Diamagnetic).
• Magnetic Permeability ($\mu$):
  This relates the total field $B$ to the magnetic intensity $H$.
  $$B = \mu H$$
  We also define Relative Permeability ($\mu_r$):
  $$\mu_r = 1 + \chi$$
  So, $\mu = \mu_0 \mu_r = \mu_0 (1 + \chi)$.

Summary Formula: The total magnetic field $B$ inside a material is the sum of the external field ($\mu_0 H$) and the field due to magnetization ($\mu_0 M$):
$$B = \mu_0 (H + M) = \mu_0 (1 + \chi) H = \mu_0 \mu_r H$$

8. Magnetic Properties of Materials

Materials are not all the same. Based on their susceptibility ($\chi$), we classify them into three major categories: Diamagnetic, Paramagnetic, and Ferromagnetic.

8.1 Diamagnetism

Behavior: Diamagnetic substances are weakly repelled by magnets. They tend to move from the stronger part of a magnetic field to the weaker part.

Explanation: This is an inherent property of all matter. When an external field is applied, the electrons orbiting the nucleus change their speed (Lenz’s law). This induces a magnetic moment opposite to the applied field, causing repulsion.

Properties:

• $\chi$ is small and negative ($-1 \le \chi < 0$).
• $\mu_r$ is slightly less than 1 ($0 \le \mu_r < 1$).
• Examples: Bismuth, Copper, Lead, Silicon, Water, Nitrogen (at STP).

Superconductors: These are the most exotic diamagnets. They have $\chi = -1$ and $\mu_r = 0$. They expel magnetic field lines completely! This phenomenon is called the Meissner Effect.

8.2 Paramagnetism

Behavior: Paramagnetic substances are weakly attracted to magnets. They move from the weaker part of the field to the stronger part.

Explanation: The atoms of these materials have a permanent magnetic dipole moment. Usually, thermal motion keeps them randomly oriented. When a field is applied, they align slightly in the direction of the field.

Properties:

• $\chi$ is small and positive ($\chi > 0$).
• $\mu_r$ is slightly greater than 1 ($\mu_r > 1$).
• Temperature Dependence: Magnetization is inversely proportional to temperature. As you cool the material, the thermal agitation decreases, and alignment improves.
• Examples: Aluminum, Sodium, Calcium, Oxygen (at STP).

8.3 Ferromagnetism

Behavior: Ferromagnetic substances are strongly attracted to magnets.

Explanation (Domain Theory): In these materials, atoms group together in macroscopic regions called Domains (size ~1mm, containing $10^{11}$ atoms). Inside a domain, all magnetic dipoles are perfectly aligned.

In an unmagnetized state, the domains are randomly oriented, canceling each other out.

When an external field $B_0$ is applied, two things happen:

1. The domains aligned with the field grow in size.
2. The other domains rotate to align with the field.

This creates a massive net magnetization.

Figure-3: (a) Randomly oriented domains result in zero net magnetism. (b) In an external field, domains align, creating strong magnetism.

Properties:

• $\chi$ is very large and positive ($\chi \gg 1$).
• $\mu_r$ is very large ($\mu_r \gg 1$).
• Examples: Iron, Cobalt, Nickel, Gadolinium.

Hard vs. Soft Ferromagnets:

Hard Magnetic Materials: Retain their magnetism even after the external field is removed. Used for making permanent magnets. Examples: Alnico (Alloy of Al, Ni, Co), Lodestone.

Soft Magnetic Materials: Lose their magnetism as soon as the field is removed. Used for electromagnets. Example: Soft Iron.

9. Solved Examples (Classroom Walkthrough)

Let’s apply what we’ve learned to solve some standard problems.

10. Summary and Key Takeaways

• Origin: Magnetic phenomena are universal. The earth behaves as a magnet with the magnetic field pointing approximately from geographic South to North.
• Dipoles: Isolated magnetic poles do not exist. The simplest magnetic element is a dipole.
• Field Lines: Magnetic field lines are continuous closed loops. They do not start or end on poles.
• Gauss’s Law: The net magnetic flux through any closed surface is zero ($\oint \mathbf{B} \cdot d\mathbf{S} = 0$).
• Materials:
  • Diamagnetic ($\chi < 0$): Repelled by magnets (e.g., Water, Copper).
  • Paramagnetic ($\chi > 0$): Weakly attracted (e.g., Aluminum).
  • Ferromagnetic ($\chi \gg 0$): Strongly attracted (e.g., Iron).
• Superconductors: Perfect diamagnets with $\chi = -1$ and $\mu_r = 0$.

11. Practice Set (CBSE Pattern)

Very Short Answer (1 Mark)

Q1. What is the unit of Magnetic Susceptibility ($\chi$)?

Ans: It is a dimensionless quantity, so it has no unit.

Q2. Where on the earth’s surface is the magnetic dip angle zero?

Ans: At the magnetic equator.

Short Answer (2-3 Marks)

Q3. A magnetic needle free to rotate in a vertical plane orients itself vertically at a certain place on Earth. What is that place?

Ans: This happens at the Magnetic Poles (North or South). Here, the horizontal component of the earth’s field is zero, so the needle aligns with the vertical component.

Q4. Explain why magnetic field lines do not intersect.

Ans: If they intersected at a point, there would be two tangents at that point, implying two directions of the magnetic field at the same location. This is physically impossible.

Long Answer (5 Marks)

Q5. (a) Define Magnetization (M) and Magnetic Intensity (H). (b) Derive the relationship between Relative Permeability ($\mu_r$) and Magnetic Susceptibility ($\chi$). (c) A paramagnetic material is cooled. How does its magnetization change?

Ans:
(a) M is magnetic moment per unit volume. H is the external magnetic field divided by $\mu_0$ minus M.
(b) Start with $B = \mu_0(H+M)$. Substitute $M = \chi H$. $B = \mu_0 H (1+\chi)$. Compare with $B = \mu H = \mu_0 \mu_r H$. Thus $\mu_r = 1 + \chi$.
(c) According to Curie’s Law, susceptibility (and thus magnetization) is inversely proportional to temperature. If cooled, thermal agitation decreases, and magnetization increases.

Case-Based Question (4 Marks)

Q6. Superconductivity: Superconductors are materials that exhibit zero electrical resistance and perfect diamagnetism when cooled below a critical temperature. This perfect diamagnetism is called the Meissner effect.

1. What is the value of $\chi$ for a superconductor? [1 Mark]

2. What happens to magnetic field lines near a superconductor? [1 Mark]

3. Why are superconductors repelled by magnets? [2 Marks]

Ans:
1. $\chi = -1$.
2. The field lines are completely expelled from the interior of the superconductor.
3. Since they are perfect diamagnets, they develop a strong opposing magnetic moment to expel the field. This opposition manifests as a repulsive force.