Quick Revision Notes: Class 12 Physics

Chapter: Magnetism and Matter

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1. Basic Concepts & Terminology

• Magnetic Dipole: An arrangement of two unlike magnetic poles of equal strength separated by a small distance.
• Magnetic Dipole Moment ($M$): It is the product of pole strength ($m$) and the magnetic length ($2l$).
  • Formula: M = m * 2l
  • SI Unit: A m^2 or J/T
  • Direction: From South pole to North pole.
• Magnetic Field Lines: Imaginary lines representing the magnetic field. They form closed loops, emerging from the North pole and entering the South pole outside the magnet.

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2. Bar Magnet as an Equivalent Solenoid

• The magnetic field of a bar magnet at large distances is identical to that of a current-carrying solenoid.
• Magnetic Moment of a Solenoid: M = N * I * A
  • where $N$ = total number of turns, $I$ = current, $A$ = cross-sectional area.

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3. Magnetic Field due to a Bar Magnet

(a) Along the Axial Line (End-on position)

For a short bar magnet of length $2l$ at distance $r$ from its centre:

• Formula: B = (mu_0 / 4_pi) * (2M / r^3)
• Direction: Along the magnetic dipole moment ($\vec{M}$).

(b) Along the Equatorial Line (Broadside-on position)

For a short bar magnet at distance $r$ from its centre:

• Formula: B = (mu_0 / 4_pi) * (M / r^3)
• Direction: Opposite to the magnetic dipole moment ($\vec{M}$).

(Note: $B_{axial} = 2 \times B_{equatorial}$ for a short magnet)

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4. Bar Magnet in a Uniform Magnetic Field

• Torque ($\tau$): When a magnetic dipole of moment $M$ is placed in a uniform magnetic field $B$ at an angle $\theta$:
  • Formula: \tau = M * B * sin(theta) or \vec{\tau} = \vec{M} \times \vec{B}
• Potential Energy ($U$): Work done in rotating the dipole in a magnetic field:
  • Formula: U = -M * B * cos(theta) or U = -\vec{M} \cdot \vec{B}
  • Special Cases:
    • Stable equilibrium ($\theta = 0^\circ$): $U = -MB$
    • Unstable equilibrium ($\theta = 180^\circ$): $U = +MB$
    • Zero energy ($\theta = 90^\circ$): $U = 0$

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5. Earth's Magnetism (Terrestrial Magnetism)

The magnetic field of the earth at any point can be resolved into three components, known as Earth's Magnetic Elements:

1. Magnetic Declination ($\theta$ or $\alpha$): The angle between the geographic meridian and the magnetic meridian at a place.
2. Magnetic Dip or Inclination ($\delta$): The angle made by the total intensity of earth's magnetic field ($B_E$) with the horizontal line in the magnetic meridian.
3. Horizontal Component ($B_H$): The component of earth's magnetic field along the horizontal direction in the magnetic meridian.
   • B_H = B_E * cos(delta)
   • Vertical component: B_V = B_E * sin(delta)
   • Total magnetic field: B_E = sqrt(B_H^2 + B_V^2)
   • Angle of dip: tan(delta) = B_V / B_H

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6. Magnetic Terms and Definitions

• Magnetic Intensity / Magnetizing Force ($H$): The degree to which a magnetic field can magnetize a substance.
  • H = B_0 / mu_0 (SI Unit: A/m)
• Intensity of Magnetization ($I$ or $M$): Magnetic moment developed per unit volume of the material.
  • I = M / V (SI Unit: A/m)
• Magnetic Induction / Magnetic Field ($B$): Total magnetic field inside the material.
  • B = mu_0 * (H + I)
• Magnetic Permeability ($\mu$): Ability of a material to allow magnetic lines of force to pass through it.
  • \mu = B / H
  • Relative Permeability ($\mu_r$): \mu_r = \mu / \mu_0
• Magnetic Susceptibility ($\chi_m$): Measure of how easily a substance can be magnetized.
  • \chi_m = I / H
  • Relation between $\mu_r$ and $\chi_m$: \mu_r = 1 + \chi_m

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7. Magnetic Properties of Materials

Property	Diamagnetic Materials	Paramagnetic Materials	Ferromagnetic Materials
Susceptibility ($\chi_m$)	Small and negative ($-1$ to $0$)	Small and positive	Large and positive ($>> 1$)
Relative Permeability ($\mu_r$)	Slightly less than $1$ ($0 \le \mu_r < 1$)	Slightly greater than $1$	Very high ($>> 1$)
Permeability ($\mu$)	Less than free space ($\mu < \mu_0$)	Slightly greater than $\mu_0$	Much greater than $\mu_0$
Effect of Magnetisng Field	Weakly repelled	Weakly attracted	Strongly attracted
Effect of Temperature	Independent of temperature	Follows Curie's Law ($\chi \propto 1/T$)	Follows Curie-Weiss Law ($\chi = C / (T - T_c)$)
Examples	Bismuth, Copper, Water, Gold	Aluminium, Sodium, Calcium	Iron, Cobalt, Nickel, Alnico

• Curie's Law: Magnetic susceptibility of a paramagnetic substance is inversely proportional to its absolute temperature ($T$).
  • \chi = C / T (where $C$ is Curie's constant).

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8. Important Board Exam Tips (MP Board)

• Always write proper SI Units with numerical answers (e.g., $A/m$ for $H$, $Tesla$ for $B$).
• Learn the vector relations clearly (e.g., $\vec{\tau} = \vec{M} \times \vec{B}$).
• Practice the derivation of $B$ on axial and equatorial lines of a bar magnet.
• Understand the graphical representation of hysteresis loop ($B-H$ curve) for ferromagnetic materials (Retentivity and Coercivity definitions are important).