Class 12 Physics Notes Chapter 5 (Magnetism and Matter) – Examplar Problems (English) Book

Detailed Notes with MCQs of Chapter 5: Magnetism and Matter. This chapter builds upon your understanding of electrostatics and introduces the concepts of magnetism, magnetic materials, and the Earth's magnetic field. Pay close attention, as these concepts are frequently tested in government exams, often through conceptual questions and direct formula applications, drawing heavily from NCERT and Exemplar problems.

Chapter 5: Magnetism and Matter - Detailed Notes

1. Introduction & Bar Magnet

• Historical Context: Natural magnets (lodestone - Fe₃O₄) were known for their attractive properties.
• Bar Magnet: A common magnetic dipole.
  • Poles: North (N) and South (S) poles exist in pairs. Isolated magnetic poles (monopoles) do not exist.
  • Magnetic Dipole Moment (m): A vector quantity representing the strength and orientation of the magnet.
    • Magnitude: m = qm * 2l, where qm is the pole strength and 2l is the magnetic length (distance between poles, slightly less than geometric length).
    • Direction: From the South pole to the North pole inside the magnet.
    • SI Unit: Ampere-meter² (A m²) or Joule/Tesla (J/T).
• Magnetic Field Lines: Imaginary lines representing the magnetic field (B).
  • Properties:
    • Form continuous closed loops (unlike electric field lines).
    • Direction: North pole to South pole outside the magnet; South pole to North pole inside the magnet.
    • Tangent at any point gives the direction of B at that point.
    • Density of lines indicates the strength of the magnetic field.
    • They never intersect each other.

2. Bar Magnet as an Equivalent Solenoid

• A current-carrying solenoid behaves like a bar magnet.
• The magnetic field lines of a finite solenoid resemble those of a bar magnet.
• The magnetic dipole moment of a solenoid with N turns, area A, carrying current I is m = NIA.

3. Magnetic Dipole in a Uniform Magnetic Field (B)

• Torque (τ): Experiences a torque that tends to align it with the field.
  • τ = m B sinθ or in vector form: **τ** = **m** x **B**
  • θ is the angle between m and B.
  • Torque is maximum when θ = 90° (τ_max = mB) and zero when θ = 0° or 180° (equilibrium positions).
• Potential Energy (U): Stored potential energy due to its orientation in the field.
  • U = -m B cosθ or in vector form: U = -**m** . **B**
  • Stable Equilibrium: θ = 0°, U = -mB (minimum potential energy).
  • Unstable Equilibrium: θ = 180°, U = +mB (maximum potential energy).

4. Gauss's Law for Magnetism

• The net magnetic flux through any closed surface is always zero.
  • ∮ **B** . d**S** = 0
• Significance: This mathematically implies the non-existence of magnetic monopoles. Magnetic field lines always form closed loops.

5. The Earth's Magnetism

• The Earth behaves like a large magnet, though its field is weak (order of 10⁻⁵ T).
• Origin: Believed to be due to electric currents produced by the convective motion of metallic fluids (mostly molten iron and nickel) in the Earth's outer core (Dynamo Effect). The magnetic axis is tilted approx. 11.3° with respect to the Earth's rotational axis.
• Elements of Earth's Magnetic Field: Three quantities required to specify the magnetic field at a location:
  • (a) Magnetic Declination (D): The angle between the geographic meridian (true north-south direction) and the magnetic meridian (direction shown by a compass needle) at a place.
  • (b) Angle of Dip or Inclination (I): The angle that the Earth's total magnetic field (B_E) makes with the horizontal direction in the magnetic meridian. At magnetic equator, I = 0°; at magnetic poles, I = 90°.
  • (c) Horizontal Component (B_H): The component of the Earth's total magnetic field along the horizontal direction in the magnetic meridian.
    • B_H = B_E cos I
    • Vertical Component B_V = B_E sin I
    • tan I = B_V / B_H
    • B_E = √(B_H² + B_V²)

6. Magnetic Properties of Materials

• Key Terms:
  • Magnetic Intensity or Magnetizing Field (H): Degree to which a magnetic field can magnetize a material. It depends only on the external source, not the medium. SI Unit: Ampere/meter (A/m).
  • Magnetization (M): Net magnetic dipole moment developed per unit volume of the material when placed in a magnetizing field. SI Unit: Ampere/meter (A/m).
  • Magnetic Susceptibility (χ): A dimensionless quantity indicating how easily a material can be magnetized. M = χ H.
  • Magnetic Permeability (μ): Ability of a material to permit the passage of magnetic field lines through it. B = μ H. SI Unit: Tesla-meter/Ampere (T m/A) or Henry/meter (H/m).
  • Relative Permeability (μᵣ): Ratio of the permeability of the medium to the permeability of free space (μ₀). μᵣ = μ / μ₀. It is dimensionless.
• Relation between B, H, and M:
  • The net magnetic field inside a material is the sum of the external field (related to H) and the field due to magnetization (related to M).
  • **B** = μ₀ (**H** + **M**)
• Relation between μᵣ and χ:
  • Since B = μH and M = χH, substituting into the above relation:
  • μH = μ₀(H + χH)
  • μH = μ₀H(1 + χ)
  • μ / μ₀ = 1 + χ
  • μᵣ = 1 + χ

7. Classification of Magnetic Materials

• (a) Diamagnetic Materials:
  • Origin: Induced magnetic dipole moments in atoms oppose the external field (Lenz's Law).
  • Properties:
    • Weakly repelled by magnets.
    • Move from stronger to weaker parts of a non-uniform field.
    • χ is small and negative (e.g., -10⁻⁵).
    • μᵣ is slightly less than 1.
    • Susceptibility is independent of temperature.
  • Examples: Bismuth, Copper, Lead, Silicon, Nitrogen (STP), Water, Sodium Chloride.
• (b) Paramagnetic Materials:
  • Origin: Atoms/molecules have permanent magnetic dipole moments, randomly oriented. External field partially aligns them.
  • Properties:
    • Weakly attracted by magnets.
    • Move from weaker to stronger parts of a non-uniform field.
    • χ is small and positive (e.g., +10⁻⁵ to +10⁻³).
    • μᵣ is slightly greater than 1.
    • Susceptibility varies inversely with absolute temperature (χ ∝ 1/T - Curie's Law).
  • Examples: Aluminium, Sodium, Calcium, Oxygen (STP), Copper Chloride.
• (c) Ferromagnetic Materials:
  • Origin: Atoms have permanent magnetic moments which strongly interact with neighbours to spontaneously align in macroscopic regions called 'domains'. External field aligns these domains.
  • Properties:
    • Strongly attracted by magnets.
    • χ is large and positive (e.g., > 1000).
    • μᵣ is large (>> 1).
    • Exhibit Hysteresis (discussed below).
    • Above a certain temperature (Curie Temperature, T_c), they lose ferromagnetic properties and behave like paramagnetic materials. Above T_c, χ ∝ 1/(T - T_c) (Curie-Weiss Law).
  • Examples: Iron, Cobalt, Nickel, Gadolinium, alloys like Alnico.

8. Hysteresis

• The phenomenon where the magnetic field (B) or magnetization (M) inside a ferromagnetic material lags behind the magnetizing field (H) when taken through a cycle of magnetization and demagnetization.
• B-H Curve (Hysteresis Loop):
  • Plot of B versus H for a ferromagnetic material as H is varied.
  • Retentivity (or Remanence): The value of B remaining when H is reduced to zero. Represents the ability to retain magnetism.
  • Coercivity: The value of reverse H required to reduce B (or M) to zero. Represents the resistance to demagnetization.
  • Area of the Loop: Represents the energy dissipated as heat per unit volume per cycle of magnetization.
• Significance:
  • Permanent Magnets: Require materials with high retentivity, high coercivity, and a broad hysteresis loop (e.g., Steel, Alnico, Cobalt Steel). They should retain magnetism strongly and resist demagnetization.
  • Electromagnets & Transformer Cores: Require materials with low retentivity, low coercivity, high permeability, and a narrow hysteresis loop (e.g., Soft Iron). This minimizes energy loss (hysteresis loss) during repeated cycles of magnetization and demagnetization.

Multiple Choice Questions (MCQs)

1. The net magnetic flux through any closed surface is:
   (a) μ₀I
   (b) Positive
   (c) Zero
   (d) Negative

2. The direction of the magnetic dipole moment (m) of a bar magnet is:
   (a) From N pole to S pole outside the magnet
   (b) From S pole to N pole inside the magnet
   (c) Perpendicular to the axis of the magnet
   (d) Along the direction of the magnetic field it produces

3. A paramagnetic sample shows a net magnetisation of 8 A/m when placed in an external magnetic field of 0.6 T at a temperature of 4 K. When the same sample is placed in an external magnetic field of 0.2 T at a temperature of 16 K, the magnetisation will be:
   (a) 32/3 A/m
   (b) 2/3 A/m
   (c) 6 A/m
   (d) 2.4 A/m

4. Which of the following statements is correct regarding diamagnetic materials?
   (a) They are strongly attracted by magnetic fields.
   (b) Their relative permeability (μᵣ) is slightly greater than 1.
   (c) Their magnetic susceptibility (χ) is small and negative.
   (d) Their magnetic susceptibility increases with temperature.

5. The angle of dip at a place where the horizontal and vertical components of the Earth's magnetic field are equal is:
   (a) 0°
   (b) 30°
   (c) 45°
   (d) 90°

6. Materials suitable for making permanent magnets should have:
   (a) High retentivity and high coercivity
   (b) Low retentivity and low coercivity
   (c) High retentivity and low coercivity
   (d) Low retentivity and high coercivity

7. Above the Curie temperature, a ferromagnetic material behaves like a:
   (a) Diamagnetic material
   (b) Paramagnetic material
   (c) Superconductor
   (d) Insulator

8. The area of the B-H hysteresis loop for a ferromagnetic material represents:
   (a) Retentivity of the material
   (b) Coercivity of the material
   (c) Energy loss per unit volume per cycle
   (d) Magnetic permeability of the material

9. A bar magnet of magnetic moment m is placed in a uniform magnetic field B. The torque experienced by the magnet is maximum when the angle between m and B is:
   (a) 0°
   (b) 45°
   (c) 90°
   (d) 180°

10. Gauss's law for magnetism (∮ **B** . d**S** = 0) signifies that:
    (a) Magnetic field lines are always straight lines.
    (b) Magnetic monopoles exist.
    (c) Magnetic field lines form continuous closed loops.
    (d) The net charge enclosed by the surface is zero.

Answer Key:

1. (c)
2. (b)
3. (b) [Hint: Magnetization M ∝ B/T for paramagnets (Curie's Law approximation for small B/T). M₂/M₁ = (B₂/T₂) / (B₁/T₁). M₂ = M₁ * (B₂/B₁) * (T₁/T₂) = 8 * (0.2/0.6) * (4/16) = 8 * (1/3) * (1/4) = 2/3 A/m]
4. (c)
5. (c) [Hint: tan I = B_V / B_H. If B_V = B_H, tan I = 1, so I = 45°]
6. (a)
7. (b)
8. (c)
9. (c) [Hint: τ = mB sinθ. sinθ is maximum (1) when θ = 90°]
10. (c)

Make sure you understand the underlying concepts behind each point and MCQ. Refer back to your NCERT textbook and Exemplar problems for further practice and clarification. Good luck with your preparation!