🧲 MAGNETISM & MATTER · Magnetic Materials & Earth's Magnetism
Bar magnet • Magnetic field lines • Magnetisation • Hysteresis • Para/Dia/Ferro • Earth's magnetism • NEET problems
🧲 BAR MAGNET & FIELD LINES
Magnetic dipole moment: m = pole strength × length (A·m²).
Field along axis: B = (μ₀/4π) × (2m/r³)
Field on equatorial line: B = (μ₀/4π) × (m/r³)
Direction: from south to north inside, north to south outside.
📈 Field lines of a bar magnet
📊 MAGNETISATION & MAGNETIC INTENSITY
Magnetisation M = net magnetic moment per unit volume (A/m).
Magnetic field intensity H = B/μ₀ – M (or H = B/μ₀ in vacuum).
Relation: B = μ₀(H + M).
Magnetic susceptibility χ = M/H (dimensionless).
Relative permeability μr = B/(μ₀H) = 1 + χ.
🔍 CLASSIFICATION OF MAGNETIC MATERIALS
Diamagnetic
χ < 0, μr < 1 (small negative).
Examples: Bi, Cu, Water, Diamond.
Field lines repelled; no permanent dipole.
Paramagnetic
χ > 0 small, μr > 1 (slightly positive).
Examples: Al, Pt, Mn, O₂.
χ ∝ 1/T (Curie's law). Field lines attracted.
Ferromagnetic
χ >> 0, μr >> 1 (large positive).
Examples: Fe, Ni, Co, Gadolinium.
Domain structure, hysteresis, Curie temperature.
📉 HYSTERESIS & ENERGY LOSS
B-H curve for ferromagnetic materials shows lag between magnetisation and applied field.
Retentivity (Br): residual magnetisation when H=0.
Coercivity (Hc): reverse field needed to demagnetise.
Area of hysteresis loop = energy loss per cycle (heat).
🖍️ B-H hysteresis loop
🌍 EARTH'S MAGNETISM
Earth acts like a giant bar magnet with magnetic south near geographic north (and vice versa).
Elements of Earth's field:
• Declination (δ): angle between geographic and magnetic meridians.
• Inclination (dip angle θ): angle made by B with horizontal.
• Horizontal component BH = B cosθ, vertical component BV = B sinθ.
At equator: θ = 0°, BH = B, BV = 0.
At poles: θ = 90°, BH = 0, BV = B.
📐 Earth's magnetic field & dip angle
💾 MAGNETIC POTENTIAL ENERGY
Potential energy of a magnetic dipole in uniform B: U = –m·B = –mB cosθ.
Torque on dipole: τ = m × B → magnitude τ = mB sinθ.
Work done to rotate dipole from θ₁ to θ₂: W = mB (cosθ₁ – cosθ₂).
💡 NEET TIPS & SHORTCUTS
- Diamagnetic materials have negative susceptibility, independent of temperature.
- Paramagnetic susceptibility follows Curie's law: χ ∝ 1/T.
- Ferromagnetic materials have domains; above Curie temperature they become paramagnetic.
- For a bar magnet, field at axial point is double that at equatorial point at same distance.
⚠️ COMMON MISTAKES
- Confusing magnetic field lines direction inside vs outside magnet.
- Using χ = μr – 1 incorrectly for diamagnetic (χ negative).
- Forgetting that earth's magnetic north is actually a magnetic south pole.
- Applying torque formula without proper sign for potential energy.
📌 QUICK REVISION CARD
Magnetic dipole moment: m = pole strength × length
Axial field (bar magnet): B = μ₀ m/(2πr³)
Equatorial field: B = μ₀ m/(4πr³)
B = μ₀(H + M)
χ = M/H, μr = 1 + χ
Torque: τ = mB sinθ
Potential: U = –mB cosθ
🧲 MAGNETISM · Moving Charges & Magnetism + Magnetism & Matter
Biot‑Savart • Ampere's law • Force on moving charge • Torque on loop • Galvanometer • Magnetic materials • Earth's magnetism • NEET problems
🔍 BIOT‑SAVART LAW & FIELD DUE TO WIRES
dB = (μ₀/4π) (I dl × r̂)/r²
Infinite straight wire: B = μ₀I/(2πr) (right‑hand thumb rule).
Circular loop (center): B = μ₀I/(2R); for N loops: B = μ₀NI/(2R).
Solenoid (inside): B = μ₀nI (n = turns/m).
Toroid: B = μ₀NI/(2πr).
🖍️ Field lines around a straight wire
⚡ FORCE ON CHARGES & CONDUCTORS
Lorentz force: F = q(v × B) → magnitude F = qvB sinθ.
Circular motion: r = mv/(qB), T = 2πm/(qB), f = qB/(2πm).
Force on current-carrying wire: F = I L × B → F = I L B sinθ.
Parallel wires: force per unit length = μ₀ I₁I₂/(2πd).
Same direction → attract, opposite → repel.
🎯 Circular path of charged particle in B field
🔄 TORQUE ON LOOP & MOVING COIL GALVANOMETER
Torque on rectangular loop in uniform B: τ = N I A B sinθ (θ = angle between area vector and B).
Magnetic moment: m = N I A; τ = m × B.
Moving coil galvanometer: τ = N I A B, opposing torque from spring τ = kθ → θ ∝ I (linear).
Current sensitivity: θ/I = NAB/k; Voltage sensitivity: θ/V = NAB/(kR).
📐 Torque on a current loop
🧲 MAGNETIC MATERIALS & PROPERTIES
Diamagnetic
χ < 0, μr < 1 (slightly repelled). e.g., Bi, Cu, water. Binside < Boutside.
Paramagnetic
χ > 0 small, μr > 1 (weakly attracted). e.g., Al, Pt. Curie law: χ ∝ 1/T.
Ferromagnetic
χ >> 0, hysteresis, Curie temperature. e.g., Fe, Ni, Co. Retain magnetization.
Magnetic susceptibility χ = μr – 1. B = μ₀(H + M) = μ₀μrH, M = χH.
🌍 EARTH'S MAGNETISM
Earth behaves like a bar magnet with magnetic south near geographic north.
Elements: Declination (δ), Inclination (dip angle θ), Horizontal component BH.
BH = B cosθ, BV = B sinθ.
💡 NEET TIPS & SHORTCUTS
- For cyclotron, frequency f = qB/(2πm) independent of speed.
- Torque on a dipole in uniform B: τ = mB sinθ, potential energy U = –m·B.
- Magnetic field on the axis of a circular loop: B = μ₀ I R²/(2(R² + x²)^{3/2}).
- For a solenoid, B inside is uniform; at ends, B = μ₀ n I / 2.
⚠️ COMMON MISTAKES
- Using right‑hand rule incorrectly for direction of force.
- Confusing magnetic field lines with electric field lines.
- Applying Biot‑Savart for infinite wire without proper integration.
- Forgetting that ferromagnets have hysteresis and saturation.
📌 QUICK REVISION CARD
Biot‑Savart: dB = μ₀ I dl sinθ/(4πr²)
Infinite wire: B = μ₀I/(2πr)
Circular loop (center): B = μ₀I/(2R)
Solenoid: B = μ₀nI
Lorentz force: F = q(v × B)
Torque on loop: τ = N I A B sinθ
Magnetic moment: m = N I A
Galvanometer current sensitivity: NAB/k