Magnetism and Matter

Q: Students often confuse Magnetic Intensity ($H$) with Magnetic Field ($B$). Think of Magnetic Intensity ($H$) as the external effort you apply (like the current in a solenoid). It exists even in a vacuum. Intensity of Magnetization ($I_m$) is the material’s internal response. How many atomic dipoles aligned themselves because of $H$? Magnetic Induction ($B$) is the net result. It is the total magnetic field inside the material, combining both your external effort ($H$) and the material’s internal response ($I_m$).

If the needle is exactly vertical, it means the entire magnetic field is pointing straight down. This only happens at the magnetic poles. Therefore, the angle of dip $\delta = 90^\circ$. Since $B_H = B \cos\delta$ and $\cos(90^\circ) = 0$, the horizontal component is zero.

Q: A normal compass only shows you the horizontal direction. But Earth’s magnetic field lines actually dive into the ground at the poles and come out at the equator. A Dip Circle measures this vertical tilt, called the Angle of Dip ($\delta$). At the magnetic equator, the field lines are perfectly parallel to the ground, so $\delta = 0^\circ$ ($B_V = 0$). At the magnetic poles, the field lines plunge straight straight down, so $\delta = 90^\circ$ ($B_H = 0$).

Since $\mu_r = 800 \gg 1$, the material is Ferromagnetic. Properties: (1) They are strongly attracted by a magnet. (2) When placed in a non-uniform magnetic field, they tend to move from the weaker to the stronger part of the field. (3) Their susceptibility $\chi_m$ is large and positive.

Q: A magnetic needle free to rotate in a vertical plane aligns itself exactly vertically at a certain place on the earth. What are the values of angle of dip and the horizontal component of Earth’s magnetic field at this place? [1 mark]

Given: $B_H = B$, $\delta = 60^\circ$. We know $\tan\delta = \frac{B_V}{B_H}$. $\tan(60^\circ) = \frac{B_V}{B} \implies B_V = B\sqrt{3}$. Total magnetic field $B_{net} = \sqrt{B_H^2 + B_V^2} = \sqrt{B^2 + (\sqrt{3}B)^2} = \sqrt{B^2 + 3B^2} = \sqrt{4B^2} = 2B$. Alternatively, $B_H = B_{net} \cos\delta \implies B = B_{net} \cos(60^\circ) = B_{net}(1/2) \implies B_{net} = 2B$.

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Home Concept Boosters CBSE Class 12 Physics Magnetism and Matter – Concept Booster | Class 12 Physics CBSE

Table of Contents

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How to Use This Page

Read each concept carefully, then check the formula, common mistake, and exam tip before moving to the next. This page covers Magnetism and Matter completely for CBSE Class 12 Physics.

Key Concepts

Class 12 · Physics · Magnetism and Matter

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Core concepts you must know

Class 12 · Ch 5

Magnetic Dipole Moment & Current Loop Formula

A current loop behaves like a magnetic dipole. For a bar magnet, it is the product of pole strength ($m$) and magnetic length ($2\vec{l}$).

$$\vec{M} = m \times (2\vec{l}) \quad | \quad B = \frac{\mu_0}{4 \pi} \frac{2M}{x^3} \text{ (Far point)}$$

Gyromagnetic Ratio & Bohr Magneton Formula

The ratio of magnetic moment to orbital angular momentum of an electron. The Bohr magneton is the minimum magnetic moment of a revolving electron.

$$\frac{\mu_e}{l} = \frac{e}{2m_e} \quad | \quad (\mu_e)_{\text{min}} = \frac{eh}{4 \pi m_e} = 9.27 \times 10^{-24} \text{ Am}^2$$

Magnetic Field of a Bar Magnet Formula

The magnetic field produced at a point on the axial line and equatorial line of a bar magnet. Notice it is exactly analogous to an electric dipole.

$$\text{Axial: } B_{\text{axial}} = \frac{\mu_0}{4 \pi} \left[ \frac{2Mr}{(r^2 – l^2)^2} \right] \xrightarrow{l \ll r} \frac{\mu_0}{4 \pi} \frac{2M}{r^3}$$

$$\text{Equatorial: } B_{eq} = \frac{\mu_0}{4 \pi} \left[ \frac{M}{(r^2 + l^2)^{3/2}} \right] \xrightarrow{l \ll r} \frac{\mu_0}{4 \pi} \frac{M}{r^3}$$

Gauss’s Law in Magnetism Formula

The net magnetic flux through any closed surface is always zero. This establishes that isolated magnetic monopoles do not exist.

$$\oint_S \vec{B} \cdot d\vec{S} = 0 \quad | \quad \phi = \vec{B} \cdot \Delta\vec{S}$$

Earth’s Magnetism: Magnetic Dip (Inclination) Formula

The angle ($\delta$) that the total magnetic field of the Earth makes with the surface of the Earth. It relates the horizontal ($B_H$) and vertical ($B_V$) components.

$$\tan \delta = \frac{B_V}{B_H}$$

Magnetization Vectors ($H$, $I_m$, $B$) Formula

Magnetic Intensity ($H$) is the external field. Intensity of Magnetization ($I_m$) is the induced dipole moment per unit volume. Total Magnetic Induction ($B$) is their combined effect.

$$H = \frac{B_0}{\mu_0} = nI \quad | \quad I_m = \frac{M}{V} \quad | \quad B = \mu_0(H + I_m)$$

Permeability & Susceptibility Formula

Susceptibility ($\chi_m$) shows how easily a substance gets magnetized. Permeability ($\mu$) is the degree to which lines of force can penetrate a material.

$$\chi_m = \frac{I_m}{H} \quad | \quad \mu = \frac{B}{H} \quad | \quad \mu_r = \frac{\mu}{\mu_0} = 1 + \chi_m$$

Curie’s Law Formula

For paramagnetic materials, the magnetic susceptibility is inversely proportional to the absolute temperature $T$. (As temperature rises, thermal agitation disrupts magnetic alignment).

$$\chi_m = \frac{C \mu_0}{T}$$

Concept Deep Dive

Understanding $H$, $I_m$, and $B$

The “Cause”, the “Response”, and the “Result”

Core Concept

Students often confuse Magnetic Intensity ($H$) with Magnetic Field ($B$).

Think of Magnetic Intensity ($H$) as the external effort you apply (like the current in a solenoid). It exists even in a vacuum.
Intensity of Magnetization ($I_m$) is the material’s internal response. How many atomic dipoles aligned themselves because of $H$?
Magnetic Induction ($B$) is the net result. It is the total magnetic field inside the material, combining both your external effort ($H$) and the material’s internal response ($I_m$).

$$B = \mu_0(H + I_m)$$

Everyday Analogy

Imagine pushing a broken-down car. $H$ is how hard you push. $I_m$ is how much your friends inside the car lean forward to help. $B$ is the total speed the car actually moves. The Susceptibility ($\chi_m$) simply measures how good your friends are at helping!

Earth’s Magnetic Elements

Navigating with a 3D compass

High Yield

A normal compass only shows you the horizontal direction. But Earth’s magnetic field lines actually dive into the ground at the poles and come out at the equator. A Dip Circle measures this vertical tilt, called the Angle of Dip ($\delta$).

At the magnetic equator, the field lines are perfectly parallel to the ground, so $\delta = 0^\circ$ ($B_V = 0$). At the magnetic poles, the field lines plunge straight straight down, so $\delta = 90^\circ$ ($B_H = 0$).

$$B_H = B \cos\delta \quad \text{and} \quad B_V = B \sin\delta$$

$$B = \sqrt{B_H^2 + B_V^2}$$

Compare & Contrast

✗ Electric Dipole

Made of two separate charges ($+q, -q$).
Charges can be isolated (Monopoles exist).
Electric field lines do not form closed loops (Start at +, end at -).
Gauss’s Law: $\oint \vec{E} \cdot d\vec{S} = q/\varepsilon_0$.

✓ Magnetic Dipole

Made of North and South poles.
Poles can NEVER be isolated (Break a magnet, you get two magnets).
Magnetic field lines form continuous closed loops.
Gauss’s Law: $\oint \vec{B} \cdot d\vec{S} = 0$.

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Remember

Despite these physical differences, the mathematical equations for Torque, Potential Energy, Axial, and Equatorial fields are identical for both, just swap $p \rightarrow M$ and $1/4\pi\varepsilon_0 \rightarrow \mu_0/4\pi$.

Common Mistakes to Avoid

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Mistake 1

Misinterpreting Susceptibility ($\chi_m$) Signs:
Diamagnetic materials have a small, negative $\chi_m$ (they repel fields weakly).
Paramagnetic materials have a small, positive $\chi_m$ (they attract fields weakly).
Ferromagnetic materials have a large, positive $\chi_m$ (they attract fields strongly). Don’t mix these up!

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Mistake 2

Confusing Magnetic Declination with Dip: Declination is the angle between the Geographic North and Magnetic North (a horizontal error). Dip (Inclination) is the angle the magnetic field makes with the horizontal plane (a vertical tilt). They are two entirely different Earth magnetic elements.

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Mistake 3

Forgetting the constants in Curie’s Law: Curie’s Law $\chi_m = C\mu_0/T$ applies only to Paramagnetic materials. Ferromagnetic materials follow the Curie-Weiss law, and Diamagnetic materials are completely independent of temperature!

Exam Tips

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Tip 1

If a question asks: “What is the physical significance of $\oint \vec{B} \cdot d\vec{S} = 0$?”, the standard board answer is “It signifies that magnetic monopoles do not exist, and magnetic field lines form continuous closed loops.”

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Tip 2

For questions involving the relation $\mu_r = 1 + \chi_m$: Since diamagnetic materials have $-1 < \chi_m < 0$, it means their relative permeability $\mu_r$ is slightly less than 1. This is a very common 1-mark MCQ.

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Did You Know

Water, copper, and humans are entirely diamagnetic! If you place a very powerful magnet near a grape (which is mostly water), the grape will actually be repelled away. With an incredibly strong magnetic field (like 16 Tesla), scientists have even levitated a live frog using diamagnetism.

Expected Exam Questions

Board Pattern Questions

Class 12 · Magnetism and Matter · CBSE Exam

Class 12 · Physics

A magnetic needle free to rotate in a vertical plane aligns itself exactly vertically at a certain place on the earth. What are the values of angle of dip and the horizontal component of Earth’s magnetic field at this place? [1 mark]

Answer Angle of dip = $90^\circ$; Horizontal component = $0$ 📝

Explanation

If the needle is exactly vertical, it means the entire magnetic field is pointing straight down. This only happens at the magnetic poles. Therefore, the angle of dip $\delta = 90^\circ$. Since $B_H = B \cos\delta$ and $\cos(90^\circ) = 0$, the horizontal component is zero.

The relative magnetic permeability of a magnetic material is 800. Identify the nature of the magnetic material and state its two properties. [2 marks]

Answer Ferromagnetic 📝

Explanation

Since $\mu_r = 800 \gg 1$, the material is Ferromagnetic.
Properties: (1) They are strongly attracted by a magnet. (2) When placed in a non-uniform magnetic field, they tend to move from the weaker to the stronger part of the field. (3) Their susceptibility $\chi_m$ is large and positive.

At a place, the horizontal component of Earth’s magnetic field is $B$ and the angle of dip is $60^\circ$. What is the value of the vertical component and the total magnetic field of the Earth at this place? [3 marks]

Answer $B_V = \sqrt{3}B$; Total $B_{net} = 2B$ 📝

Explanation

Given: $B_H = B$, $\delta = 60^\circ$.
We know $\tan\delta = \frac{B_V}{B_H}$.
$\tan(60^\circ) = \frac{B_V}{B} \implies B_V = B\sqrt{3}$.
Total magnetic field $B_{net} = \sqrt{B_H^2 + B_V^2} = \sqrt{B^2 + (\sqrt{3}B)^2} = \sqrt{B^2 + 3B^2} = \sqrt{4B^2} = 2B$.
Alternatively, $B_H = B_{net} \cos\delta \implies B = B_{net} \cos(60^\circ) = B_{net}(1/2) \implies B_{net} = 2B$.

Concept Map