Magnetism and Matter - Formulas, Concepts, and Applications Class 12 Notes

Magnetism and Matter - Magnetism and matter are fundamental topics in physics, focusing on the interaction of magnetic fields with matter. This article delves into key concepts, definitions, and formulas essential for understanding the principles of magnetism and matter, particularly for students preparing for their exams. Let’s explore the fascinating world of magnets and magnetic fields.

What is Magnetism?

Magnetism is a force of attraction or repulsion due to the motion of charged particles, particularly electrons. It manifests in materials that have unpaired electrons and are influenced by magnetic fields.

Key Components of Magnetism:

1. Magnetic Field: The region around a magnet where magnetic forces can be observed.
2. Magnetic Moment: A measure of the strength and direction of a magnetic source.
3. Magnetic Permeability: The ability of a material to support the formation of a magnetic field within itself.

Magnetic Dipole and Magnetic Moment

Magnetic Dipole

A magnetic dipole is a system consisting of two equal and opposite magnetic poles separated by a small distance.

Magnetic Moment (m)

The magnetic moment ($m$) measures the strength of the magnetic dipole and is given by:

$$m = q_m \cdot 2l$$

Where:

• $q_m$ = Magnetic pole strength
• $2l$ = Distance between the poles

Magnetic Dipole Moment of an Electron

The magnetic dipole moment of a revolving electron is:

$$m = \frac{e \cdot v \cdot r}{2}$$

Where:

• $e$ = Charge of the electron
• $v$ = Velocity of the electron
• $r$ = Radius of the orbit

For angular momentum ($L = m \cdot v \cdot r$):

$$M = \frac{e \cdot L}{2m_e}$$

Where $m_e$ is the mass of the electron.

Magnetic Field

A magnetic field ($B$) represents the area of influence around a magnet where magnetic forces are experienced.

Gauss Law for Magnetism

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

This law states that the net magnetic flux through any closed surface is zero because magnetic monopoles do not exist.

Potential Energy in a Magnetic Dipole

The potential energy ($U$) of a magnetic dipole in a magnetic field is:

$$U = -m \cdot B \cdot \cos \theta$$

Where:

• $m$ = Magnetic moment
• $B$ = Magnetic field strength
• $\theta$ = Angle between $m$ and $B$

Earth's Magnetism

The Earth behaves like a giant bar magnet, with its magnetic field resembling that of a dipole.

Key Terms:

1. Magnetic Equator: A flat circle dividing the Earth into two hemispheres where the magnetic field is horizontal.
2. Magnetic Declination ($\alpha$): The angle between the magnetic meridian and the geographical meridian.
3. Angle of Dip ($\delta$): The angle made by the Earth’s total magnetic field with the horizontal direction.

Horizontal and Vertical Components of Earth's Magnetic Field:

$$B_H = B \cdot \cos \theta$$ $$B_V = B \cdot \sin \theta$$

Resultant magnetic field:

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

Magnetic Field in a Solenoid

The magnetic field inside a long solenoid is given by:

$$B_0 = \mu_0 \cdot n \cdot I$$

Where:

• $\mu_0$: Permeability of free space ($4\pi \times 10^{-7} \, T \cdot m/A$)
• $n$: Number of turns per unit length
• $I$: Current through the solenoid

Magnetic Induction

Magnetic induction ($B$) is the total magnetic field produced in a material.

$$B = B_0 + B_M$$

Where:

• $B_0$: Magnetic field in free space
• $B_M$: Magnetic field due to magnetization

Magnetizing Field Intensity

The magnetizing field intensity ($H$) is:

$$H = \frac{B_0}{\mu_0}$$

Intensity of Magnetization

The intensity of magnetization ($M$) is:

$$M = \frac{m}{V}$$

Where:

• $m$: Magnetic moment
• $V$: Volume

Magnetic Permeability and Susceptibility

Magnetic Permeability ($\mu$)

$$\mu = \frac{B}{H}$$

Relative Permeability ($\mu_r$)

$$\mu_r = \frac{\mu}{\mu_0}$$

Magnetic Susceptibility ($\chi_m$)

$$\chi_m = \frac{M}{H}$$

Relation Between Permeability and Susceptibility

$$\mu_r = 1 + \chi_m$$

Work Done in Rotating a Magnetic Dipole

The work done ($W$) in rotating a magnetic dipole in a magnetic field is:

$$W = MB (\cos \theta_1 - \cos \theta_2)$$

Where:

• $\theta_1, \theta_2$: Initial and final angles of rotation

Applications of Magnetism

1. Navigation: Earth's magnetic field helps in compass navigation.
2. Magnetic Storage: Used in data storage devices like hard drives.
3. Electric Motors and Generators: Magnetic fields are essential in converting electrical energy to mechanical energy and vice versa.

FAQs About Magnetism and Matter

1. What is the magnetic dipole moment?

The magnetic dipole moment measures the strength and orientation of a magnetic source. It is given by $m = q_m \cdot 2l$.

2. What is the significance of Earth's magnetic field?

Earth's magnetic field protects us from harmful solar radiation and aids in navigation.

3. What is magnetic susceptibility?

Magnetic susceptibility ($\chi_m$) quantifies how easily a material can be magnetized in a magnetic field.

4. What is Gauss Law for Magnetism?

Gauss Law states that the total magnetic flux through a closed surface is zero because magnetic monopoles do not exist.

5. What is the angle of dip?

The angle of dip ($\delta$) is the angle made by the Earth's magnetic field with the horizontal plane.

6. How is the magnetic field inside a solenoid calculated?

The magnetic field inside a solenoid is given by $B_0 = \mu_0 \cdot n \cdot I$.