Class 12 Physics Notes Chapter 5 (Magnetism and matter) – Physics Part-I Book

Alright class, let's delve into Chapter 5: Magnetism and Matter. This chapter builds upon our understanding of magnetic effects due to currents and explores magnetism as an intrinsic property of matter, including the Earth's magnetic field. Pay close attention, as these concepts are frequently tested in various government examinations.

Chapter 5: Magnetism and Matter - Detailed Notes

1. Introduction & The Bar Magnet

• Historical Context: Natural magnets (lodestones - ores of iron oxide) were known since ancient times. The directive property (aligning North-South) led to the invention of the magnetic compass.
• Bar Magnet:
  • A rectangular piece of a ferromagnetic material (like iron) showing permanent magnetic properties.
  • Poles: Two points, usually near the ends, where the magnetic strength is concentrated – North pole (N) and South pole (S).
  • Properties:
    • Attractive Property: Attracts small pieces of iron, nickel, cobalt, etc.
    • Directive Property: A freely suspended magnet aligns itself approximately along the geographic North-South direction. The pole pointing towards geographic North is the North-seeking pole (or North pole), and the one pointing towards geographic South is the South-seeking pole (or South pole).
    • Like poles repel, unlike poles attract.
    • Magnetic poles always exist in pairs (N-S). Isolated magnetic poles (monopoles) do not exist.
    • Magnetic strength is maximum at the poles and minimum at the center.
    • Induces magnetism in nearby magnetic materials.

2. Magnetic Field Lines

• Imaginary lines used to represent the magnetic field visually. The tangent at any point gives the direction of the net magnetic field B at that point.
• Properties:
  • They form continuous closed loops, emerging from the North pole and entering the South pole outside the magnet, and running from South to North inside the magnet.
  • The density of field lines (number of lines per unit area) represents the strength of the magnetic field. Denser lines indicate a stronger field.
  • They never intersect each other. (If they did, there would be two directions of the magnetic field at the point of intersection, which is impossible).
  • They tend to contract longitudinally (explaining attraction between unlike poles) and exert lateral pressure (explaining repulsion between like poles).

3. 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 field at a far axial point of a solenoid of length 2l, radius a, n turns per unit length, carrying current I is given by:
  **B_axial ≈ (μ₀ / 4π) * (2m / r³) ** where r is the distance from the center and m is the magnetic dipole moment.
• Magnetic Dipole Moment (m): For a solenoid, m = N I A, where N is the total number of turns (N = n * 2l), I is the current, and A is the cross-sectional area (πa²). The direction of m is given by the Right-Hand Thumb Rule (curl fingers in the direction of current, thumb gives the direction of m, which points from S to N).

4. The Magnetic Dipole

• An arrangement of two equal and opposite magnetic poles separated by a small distance. A bar magnet and a current loop are examples.
• Magnetic Dipole Moment (m):
  • For a bar magnet: m = q_m * (2l), where q_m is the pole strength and 2l is the magnetic length (distance between poles, slightly less than geometric length). Its direction is from S to N pole. Unit: Ampere-meter² (Am²).
  • For a current loop: m = I A, where I is the current and A is the area vector of the loop. Direction is perpendicular to the plane of the loop, given by the Right-Hand Thumb Rule.
  • For an electron revolving in an orbit: m_l = - (e / 2m_e) L, where e is the electron charge, m_e is its mass, and L is its orbital angular momentum. The negative sign indicates that m_l is opposite to L.
• Magnetic Field due to a Dipole (Bar Magnet):
  • On the axial line (at distance r from the center): **B_axial = (μ₀ / 4π) * (2m / r³) ** (for r >> l)
  • On the equatorial line (at distance r from the center): **B_equatorial = -(μ₀ / 4π) * (m / r³) ** (for r >> l). The direction is opposite to m.
  • Note: |B_axial| = 2 |B_equatorial| for the same distance r.

5. Torque and Potential Energy in a Uniform Magnetic Field (B)

• Torque (τ): When a magnetic dipole m is placed in a uniform magnetic field B, it experiences a torque:
  τ = m × B = m B sinθ
  where θ is the angle between m and B. The torque tends to align m with B. Torque is maximum when θ = 90° (τ = mB) and minimum (zero) when θ = 0° or 180°.
• Potential Energy (U): The potential energy of a magnetic dipole in a uniform magnetic field is:
  U = - m ⋅ B = - m B cosθ
  • Minimum potential energy (most stable) when θ = 0° (U = -mB), m parallel to B.
  • Maximum potential energy (most unstable) when θ = 180° (U = +mB), m antiparallel to B.
  • Zero potential energy when θ = 90°, m perpendicular to B.

6. Gauss's Law for Magnetism

• Statement: The net magnetic flux (Φ_B) through any closed surface is always zero.
  ∮ B ⋅ dA = 0
• Significance: This implies that magnetic monopoles (isolated N or S poles) do not exist. Magnetic field lines always form closed loops.

7. Earth's Magnetism (Geomagnetism)

• The Earth behaves as if a giant bar magnet is placed roughly along its axis of rotation, with its magnetic South pole near the geographic North pole and its magnetic North pole near the geographic South pole.
• Origin: Believed to be due to the "Dynamo Effect" - electric currents generated by the convective motion of metallic fluids (mostly molten iron and nickel) in the Earth's outer core.
• Magnetic Elements: Three quantities required to specify the Earth's magnetic field at a place:
  • Magnetic Declination (D or α): The angle between the geographic meridian and the magnetic meridian at a place. It specifies the deviation of the compass needle from the true North-South direction.
  • Angle of Dip or Inclination (I or δ): The angle that the Earth's total magnetic field (B_E) makes with the horizontal direction in the magnetic meridian. It's the angle shown by a dip needle. At magnetic equator, I = 0°; at magnetic poles, I = 90°.
  • Horizontal Component of Earth's Magnetic Field (H_E or B_H): The component of B_E along the horizontal direction in the magnetic meridian.
• Relations:
  • H_E = B_E cos I
  • Vertical Component (Z_E or B_V) = B_E sin I
  • tan I = Z_E / H_E
  • B_E = √(H_E² + Z_E²)

8. Magnetisation and Magnetic Intensity

• When a material is placed in a magnetic field, it gets magnetized.
• Magnetisation (M): The net magnetic dipole moment developed per unit volume of the material.
  M = m_net / V
  Unit: Ampere/meter (A/m). It's a vector quantity.
• Magnetic Intensity (H) or Magnetising Field: This represents the degree to which a magnetic field can magnetize a material. It is related to the external field sources (like current in a solenoid) and is independent of the medium's properties.
  In vacuum, B₀ = μ₀ H. Unit: Ampere/meter (A/m).
• Relation between B, H, and M: The total magnetic field B inside a material is the sum of the field due to external sources (B₀ = μ₀ H) and the field due to the induced magnetisation (B_m = μ₀ M).
  B = B₀ + B_m = μ₀ (H + M)
• Magnetic Susceptibility (χ): A dimensionless quantity that measures how easily a material can be magnetized.
  M = χ H
  Materials with larger χ are more easily magnetized.
• Magnetic Permeability (μ): The ability of a material to permit the passage of magnetic field lines through it.
  B = μ H
  Unit: Tesla-meter/Ampere (Tm/A) or Henry/meter (H/m).
• Relative Permeability (μᵣ): The ratio of the permeability of the medium (μ) to the permeability of free space (μ₀).
  μᵣ = μ / μ₀ (Dimensionless)
• Relations between μ, μᵣ, and χ:
  Substituting M = χH in B = μ₀(H + M), we get B = μ₀(H + χH) = μ₀(1 + χ)H.
  Comparing with B = μH, we get μ = μ₀(1 + χ).
  Therefore, μᵣ = 1 + χ

9. Classification of Magnetic Materials

Based on their behaviour in an external magnetic field (or their values of χ and μᵣ):

• Curie's Law (Paramagnetism): The magnetisation (M) or susceptibility (χ) of a paramagnetic material is inversely proportional to the absolute temperature (T). M ∝ B_ext / T or χ ∝ 1/T.
• Curie Temperature (T_c): The temperature above which a ferromagnetic material becomes paramagnetic.
• Hysteresis (Ferromagnetism): The lagging of magnetisation (M) or magnetic field (B) behind the magnetising field (H) when a ferromagnetic material is subjected to a cycle of magnetisation.
  • Hysteresis Loop: A plot of B (or M) versus H for a ferromagnetic material undergoing a cycle. The area of the loop represents the energy loss per unit volume per cycle (as heat).
  • Retentivity (or Remanence): The value of B or M remaining when H is reduced to zero. It indicates the ability to retain magnetism.
  • Coercivity: The value of reverse H required to reduce B or M to zero. It indicates the resistance to demagnetisation.

10. Permanent Magnets and Electromagnets

• Permanent Magnets: Materials that retain their ferromagnetic properties for a long time.
  • Requirements: High Retentivity, High Coercivity, High Permeability. Large hysteresis loop area.
  • Materials: Steel, Alnico (Al-Ni-Co-Fe alloy), Cobalt Steel, Ticonal.
• Electromagnets: Magnets whose magnetism exists only as long as current flows through the coil wound around them. Usually have a soft iron core.
  • Requirements: High Permeability, Low Retentivity, Low Coercivity. Narrow hysteresis loop area (to minimize energy loss).
  • Materials: Soft Iron. Used in electric bells, loudspeakers, telephone diaphragms, cranes.

Important Formulas Summary:

• m = q_m * (2l) ; m = NIA
• B_axial = (μ₀/4π) * (2m/r³) ; B_eq = -(μ₀/4π) * (m/r³)
• τ = m × B = mB sinθ
• U = - m ⋅ B = -mB cosθ
• ∮ B ⋅ dA = 0 (Gauss's Law)
• H_E = B_E cos I ; Z_E = B_E sin I ; tan I = Z_E / H_E
• B = μ₀ (H + M)
• M = χ H
• B = μ H
• μ = μ₀ μᵣ
• μᵣ = 1 + χ
• Curie's Law: χ ∝ 1/T (Paramagnetic)

Multiple Choice Questions (MCQs)

1. The magnetic field lines due to a bar magnet:
   a) Emerge from the South pole and enter the North pole.
   b) Form closed loops.
   c) Intersect each other near the poles.
   d) Are denser near the center of the magnet.

2. The SI unit of magnetic dipole moment (m) is:
   a) Ampere/meter (A/m)
   b) Tesla (T)
   c) Ampere-meter² (Am²)
   d) Weber (Wb)

3. Gauss's law for magnetism (∮ B ⋅ dA = 0) signifies that:
   a) Magnetic field is conservative.
   b) Magnetic monopoles do not exist.
   c) Magnetic field lines are always straight.
   d) Magnetic flux through any surface is zero.

4. At the magnetic poles of the Earth, the angle of dip (I) is:
   a) 0°
   b) 45°
   c) 90°
   d) 180°

5. Which of the following materials is diamagnetic?
   a) Aluminum
   b) Iron
   c) Copper
   d) Nickel

6. The relation between relative permeability (μᵣ) and magnetic susceptibility (χ) is:
   a) μᵣ = 1 + χ
   b) μᵣ = 1 - χ
   c) μᵣ = χ - 1
   d) μᵣ = 1 / χ

7. Curie's law (χ ∝ 1/T) is obeyed by:
   a) Diamagnetic materials
   b) Paramagnetic materials
   c) Ferromagnetic materials
   d) All magnetic materials

8. A material 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

9. The potential energy of a magnetic dipole (m) in a uniform magnetic field (B) is minimum when the angle between m and B is:
   a) 0°
   b) 90°
   c) 180°
   d) 270°

10. A soft iron core is used in electromagnets because it has:
    a) Low permeability and high retentivity
    b) High permeability and low retentivity
    c) Low permeability and low retentivity
    d) High permeability and high retentivity

Answers to MCQs:

1. b) Form closed loops.
2. c) Ampere-meter² (Am²)
3. b) Magnetic monopoles do not exist.
4. c) 90°
5. c) Copper
6. a) μᵣ = 1 + χ
7. b) Paramagnetic materials
8. a) High retentivity and high coercivity
9. a) 0°
10. b) High permeability and low retentivity

Revise these notes thoroughly. Focus on the definitions, properties, formulas, and the distinctions between different types of magnetic materials. Understanding the Earth's magnetic elements and the concept of hysteresis is also very important. Good luck with your preparation!