Detailed Notes: Class 12 Physics Chapter 5 - Magnetism and Matter
These notes are based on the NCERT syllabus for CBSE Class 12 Physics (updated for 2025-26). They provide in-depth explanations, derivations, formulas, and key concepts for comprehensive understanding and revision. Structured section-wise, with embedded diagrams from public educational sources for visual aid. Important formulas are highlighted, and examples/numericals hints are included where relevant.
1. Introduction to the Bar Magnet and Magnetic Dipole
1.1 Bar Magnet
A bar magnet is a rectangular piece of ferromagnetic material (e.g., steel, iron) that exhibits magnetic properties with two distinct poles: North (N) pole and South (S) pole.
- Key Properties:
- Like poles repel, unlike poles attract (Coulomb's inverse square law applies).
- Poles always occur in pairs; isolated poles (monopoles) do not exist.
- Magnetic length (2ℓ): Distance between the two effective poles, slightly less than the geometric length (2L), typically ℓ ≈ 0.9L due to pole contraction.
- Neutral Points: Points where the net magnetic field is zero, e.g., on the equatorial line in an external uniform field.
Diagram: Bar Magnet Poles and Magnetic Length (NCERT Fig. 5.1)
Description: Rectangular bar magnet with N pole on left, S on right. Geometric length 2L, magnetic length 2ℓ (ℓ ≈ 0.9L). Dipole moment M from S to N.
Reference: Wikimedia Commons (public domain). More at BYJU'S.
1.2 Magnetic Dipole
A magnetic dipole consists of two equal and opposite magnetic poles separated by a small distance (2ℓ).
- Magnetic Dipole Moment (M): Vector quantity pointing from S to N pole.
- Magnitude: \[ M = m \times 2\ell \], where m is pole strength (SI unit: A·m).
- For a current-carrying loop: \[ \vec{M} = I \vec{A} \], where I is current, A is area vector (perpendicular to plane, right-hand rule).
- SI Unit: A·m² or J/T (joule per tesla).
- Equivalence: A bar magnet behaves like a current loop (or solenoid) for far-field approximations.
Example: A bar magnet with pole strength 0.5 A·m and magnetic length 0.1 m has M = 0.05 A·m².
2. Coulomb's Law in Magnetism
Statement: The force between two magnetic poles is directly proportional to their pole strengths and inversely proportional to the square of the distance between them.
- Formula: \[ F = \frac{\mu_0}{4\pi} \frac{m_1 m_2}{r^2} \]
- Attractive if poles are unlike; repulsive if like.
- \[ \frac{\mu_0}{4\pi} = 10^{-7} \] T·m/A (permeability of free space constant).
- Derivation Insight: Analogous to electrostatic Coulomb's law, but magnetic (no negative poles, hence no isolated monopoles).
- Limitations: Valid only in vacuum; ignores material effects.
Numerical Hint: Calculate force between two poles m = 10 A·m at r = 0.1 m: F ≈ 10^{-5} N (repulsive if same poles).
3. Magnetic Field Lines
Definition: Imaginary lines representing the direction and strength of the magnetic field (B).
- Properties:
- Form closed continuous loops (emerge from N, enter S outside; opposite inside).
- Direction: Tangent to the line gives \(\vec{B}\) direction (from N to S outside).
- Density: Higher density indicates stronger field.
- Never intersect (unique direction at a point).
- No two lines begin/end at same point (no monopoles).
- For Bar Magnet: Crowded near poles (strong field); sparse in equatorial region.
- For Current Loop: Similar to bar magnet; field reverses inside the loop.
Diagram: Magnetic Field Lines Around Bar Magnet (NCERT Fig. 5.2)
Description: Curved lines emerge from N pole, enter S pole, forming closed loops. Dense near poles, sparse equatorially. Inside: S to N.
Reference: Wikimedia Commons. Video at YouTube.
4. Magnetic Field on the Axis and Equatorial Line of a Magnetic Dipole (Bar Magnet)
4.1 Axial Position (End-on)
Point on the axis, distance d from center (d >> ℓ).
- Field (B_A): \[ B_A = \frac{\mu_0}{4\pi} \frac{2M}{d^3} \]
- Direction: Along the axis, away from N pole (parallel to M).
- Derivation: Superposition of fields from two poles; approximates to dipole for large d.
Diagram: Axial (End-on) Position (NCERT Fig. 5.3)
Description: Point P on axis at d from center; B_axial parallel to M, from N outward.
Reference: Wikimedia Commons. See Vedantu PDF.
4.2 Equatorial Position (Broadside-on)
Point on perpendicular bisector, distance d from center (d >> ℓ).
- Field (B_E): \[ B_E = \frac{\mu_0}{4\pi} \frac{M}{d^3} = \frac{1}{2} B_A \]
- Direction: Parallel to axis but opposite to M (towards S pole).
- Comparison: B_A = 2 B_E; both decrease as 1/d³.
Diagram: Equatorial (Broadside-on) Position (NCERT Fig. 5.4)
Description: Point P on bisector; B_equatorial anti-parallel to M.
Reference: Wikimedia Commons.
Neutral Point: On equatorial line, where external B cancels bar magnet's B_E.
Numerical Hint: For M = 1 A·m², d = 0.1 m, B_A ≈ 2 × 10^{-5} T.
5. Magnetic Dipole in a Uniform Magnetic Field
5.1 Torque on a Dipole
A dipole in uniform \(\vec{B}\) experiences no net force (equal/opposite on poles) but a couple (torque).
- Formula: \[ \vec{\tau} = \vec{M} \times \vec{B} \]
- Magnitude: \[ \tau = MB \sin \theta \] (θ = angle between M and B).
- Direction: Perpendicular to plane of M and B; tends to align M with B.
- Stable Equilibrium: θ = 0° (τ = 0, minimum energy).
- Unstable Equilibrium: θ = 180°.
Diagram: Torque on Dipole in Uniform Field (NCERT Fig. 5.7)
Description: Dipole M at angle θ to B; torque τ perpendicular, aligning M with B.
Reference: Wikimedia Commons.
5.2 Potential Energy
- Formula: \[ U = -\vec{M} \cdot \vec{B} = -MB \cos \theta \]
- Minimum at θ = 0° (stable); maximum at θ = 180° (unstable); zero at θ = 90°.
- Work Done to rotate from θ₁ to θ₂: \[ W = MB (\cos \theta_1 - \cos \theta_2) \].
5.3 Oscillation of a Freely Suspended Magnet
Small angular displacement: Performs SHM in Earth's horizontal field B_H.
- Time Period: \[ T = 2\pi \sqrt{\frac{I}{MB_H}} \]
- I = moment of inertia about suspension point.
- Application: Vibration magnetometer measures M and B_H.
- Derivation Insight: τ = -MB_H sinθ ≈ -MB_H θ (small θ); like torsional pendulum.
6. Moving Coil Galvanometer and Earth's Magnetism (Connection)
In vibration magnetometer, T helps find M = (4π² I)/(T² B_H).
Earth's field used as uniform B.
7. The Moving Coil Galvanometer (Brief Link to Chapter)
Though in Chapter 4, relevant here: Torque τ = N I A B sinθ aligns with dipole torque.
8. Gauss's Law for Magnetism
Statement: The surface integral of \(\vec{B}\) over any closed surface is zero.
- Formula: \[ \oint \vec{B} \cdot d\vec{A} = 0 \]
- Implication: Magnetic field lines form closed loops; no net flux (no monopoles).
- Analogy with Electrostatics:
| Electrostatics | Magnetism |
|---|
| \[ \oint \vec{E} \cdot d\vec{A} = \frac{q}{\epsilon_0} \] | \[ \oint \vec{B} \cdot d\vec{A} = 0 \] |
| Isolated charges exist | No isolated poles |
9. Earth's Magnetism
9.1 Earth's Magnetic Field
Earth acts like a giant bar magnet (dipole moment ≈ 8 × 10²² A·m², confirmed as of 2025), but actually due to dynamo effect (molten core currents).
Total Field (B): Varies (weaker at equator ~0.3 × 10^{-4} T; stronger at poles ~0.6 × 10^{-4} T).
9.2 Magnetic Elements
- Declination (δ or θ): Angle between magnetic meridian (compass N) and geographic meridian (true N). Varies (0° at agonic line).
- Inclination or Dip Angle (δ): Angle between total B and horizontal plane.
- At magnetic equator: δ = 0° (B horizontal).
- At magnetic poles: δ = 90° (B vertical).
- Horizontal Component (B_H): \[ B_H = B \cos \delta \] (used in compasses).
- Vertical Component (B_V): \[ B_V = B \sin \delta \].
- Relations: \[ B = \frac{B_H}{\cos \delta} = B_H \sqrt{1 + \tan^2 \delta} \]; \[ \tan \delta = \frac{B_V}{B_H} \].
- Average B_H ≈ 0.3–0.6 × 10^{-4} T (India: ~0.4 × 10^{-4} T).
Diagram: Earth's Magnetic Elements (Declination & Dip)
Description: Compass showing declination θ; dip circle for inclination δ. B_H horizontal, B_V vertical.
Example: If δ = 30°, B_H = 0.3 × 10^{-4} T, then B_V ≈ 0.17 × 10^{-4} T; B ≈ 0.35 × 10^{-4} T.
Reference: Wikimedia Commons.
9.3 Measurement
- Deflection Magnetometer: Measures B_H, M (tan A/B positions).
- Vibration Magnetometer: Measures M, B_H via T.
10. Magnetism and Magnetic Properties of Materials
10.1 Basic Relations
- Magnetic Field (B): Total field inside material.
- Magnetizing Field (H): External field causing magnetization (SI unit: A/m).
- Magnetization (M): Magnetic moment per unit volume (SI unit: A/m).
- Key Relation: \[ \vec{B} = \mu_0 (\vec{H} + \vec{M}) \]
- Relative Permeability (μ_r): \[ \mu_r = \frac{B}{\mu_0 H} = 1 + \frac{M}{H} \]
- Magnetic Susceptibility (χ_m): \[ \chi_m = \frac{M}{H} \] (dimensionless).
10.2 Classification of Materials
Materials classified based on response to external H:
| Type | χ_m Value | μ_r Value | Behavior | Examples | Explanation |
|---|
| Diamagnetic | Negative, small (~ -10^{-5}) | < 1 | Weakly repelled; field lines expelled (Meissner effect in superconductors). | Bi, Cu, H₂O, Au, Ag | Induced M opposes H (Lenz's law); all materials show this weakly. |
| Paramagnetic | Positive, small (~ 10^{-5}) | >1, close to 1 | Weakly attracted; aligns with field. | Al, Cr, O₂, Pt, Mg | Atomic dipoles align with H; disordered without field. Follows Curie's Law: \[ \chi_m = \frac{C}{T} \] (C = Curie constant). |
| Ferromagnetic | Positive, large (~10²–10⁶) | >>1 | Strongly attracted; retains magnetism (domains align). | Fe, Ni, Co, Gd | Domain structure; hysteresis; Curie temperature (T_C) above which becomes paramagnetic. |
- Diamagnetism: Temperature independent; universal.
- Paramagnetism: Inverse to T.
- Ferromagnetism: Complex; Weiss theory (internal fields).
10.3 Hysteresis Loop
B-H Curve: Plot of B vs H; loop shows lag (hysteresis).
- Retentivity (Residual Magnetism): B at H=0.
- Coercivity: Reverse H to make B=0.
Soft Magnets (e.g., soft iron): Narrow loop (low coercivity, low retentivity) – for electromagnets.
Hard Magnets (e.g., steel): Wide loop (high coercivity, high retentivity) – for permanent magnets.
Energy Loss: Area of loop = energy dissipated per cycle (as heat).
Diagram: Hysteresis Loop
Description: B vs H plot; S-shaped initial curve, closed loop on cycling. Shows saturation, retentivity, coercivity.
Reference: Wikimedia Commons.
11. Permanent Magnets and Electromagnets
11.1 Permanent Magnets
Made from hard ferromagnetic materials (high coercivity); retain M without external H.
- Materials: Alnico, CrCo, ferrites.
- Demagnetization Methods: Heating above T_C, hammering, AC field.
- Limitations: Lose strength over time; cannot vary strength.
11.2 Electromagnets
Temporary magnets using soft iron core in solenoid; strength varies with I.
- Advantages: Variable strength/polarity; no residual magnetism; stronger than permanent.
- Formula for Field: \[ B = \mu_0 n I \] (inside solenoid).
Choice: Permanent for steady fields (e.g., fridge magnets); electromagnets for cranes, MRI.
Important Formulas Summary Table
| Concept | Formula | Key Notes |
|---|
| Dipole Moment | \[ M = m \cdot 2\ell = I A \] | Vector from S to N |
| Force Between Poles | \[ F = \frac{\mu_0}{4\pi} \frac{m_1 m_2}{r^2} \] | Attractive for unlike poles |
| Axial Field | \[ B_A = \frac{\mu_0}{4\pi} \frac{2M}{d^3} \] | Parallel to M |
| Equatorial Field | \[ B_E = \frac{\mu_0}{4\pi} \frac{M}{d^3} \] | Anti-parallel to M |
| Torque | \[ \tau = M B \sin \theta \] | Aligns M with B |
| Potential Energy | \[ U = - M B \cos \theta \] | Min at θ=0° |
| Oscillation Period | \[ T = 2\pi \sqrt{\frac{I}{M B_H}} \] | SHM for small θ |
| Earth's Components | \[ B_H = B \cos \delta \], \[ B_V = B \sin \delta \] | tan δ = B_V / B_H |
| B-H Relation | \[ B = \mu_0 (H + M) \], \[ \chi_m = M/H \] | μ_r = 1 + χ_m |
Tips for Exams
- Derivations: Practice axial/equatorial fields, torque from forces.
- Numericals: Focus on B calculations, T for oscillations, susceptibility.
- Conceptual: Explain why no monopoles, hysteresis importance.
- Diagrams: Draw field lines, hysteresis loop, dip circle.
- MCQs: Common on properties, classifications, Earth's elements.
For practice questions, refer to NCERT exercises. These notes cover 100% of the chapter for boards/JEE. Updated values confirmed for 2025. If you need Hindi version or expansions, let me know!
