Learning Objectives
- Understand bar magnets and their properties
- Learn about Earth's magnetism and magnetic elements
- Classify magnetic materials: diamagnetic, paramagnetic, ferromagnetic
- Understand magnetic susceptibility and permeability
- Study hysteresis and its applications
Key Concepts
Bar Magnet and Magnetic Dipole
A bar magnet behaves like a magnetic dipole. Magnetic field lines form closed loops (from N to S outside, S to N inside).
Magnetic dipole moment: M = m × 2l (m = pole strength, 2l = magnetic length).
A current loop is equivalent to a magnetic dipole: M = NIA.
Axial field: B = (μ₀/4π)(2M/r³). Equatorial field: B = (μ₀/4π)(M/r³).
Torque in uniform field: τ = M × B = MB sin θ.
Potential energy: U = -M · B = -MB cos θ.
Earth's Magnetism
Earth acts as a giant magnetic dipole. The geographic north is near the magnetic south pole.
Elements of Earth's magnetic field:
- Declination (δ): Angle between geographic and magnetic meridians.
- Dip/Inclination (I): Angle of Earth's field with horizontal. I = 0° at magnetic equator, I = 90° at magnetic poles.
- Horizontal component: B_H = B cos I
- Vertical component: B_V = B sin I
- B = √(B_H² + B_V²); tan I = B_V/B_H
Classification of Magnetic Materials
Diamagnetic (χ < 0, μᵣ < 1): Weakly repelled by magnetic field. No permanent dipole moment. Examples: bismuth, copper, water, gold, silicon. Independent of temperature.
Paramagnetic (χ > 0, μᵣ > 1, slightly): Weakly attracted. Atoms have permanent dipole moments that align partially with field. Examples: aluminium, sodium, oxygen, platinum. χ ∝ 1/T (Curie's law).
Ferromagnetic (χ >> 0, μᵣ >> 1): Strongly attracted. Domains align with field. Examples: iron, cobalt, nickel, gadolinium. Above Curie temperature, become paramagnetic.
Magnetisation and Magnetic Intensity
Magnetisation (M): Magnetic moment per unit volume. M = χH.
Magnetic intensity (H): H = B/μ₀ - M. For a solenoid: H = nI.
B = μ₀(H + M) = μ₀μᵣH = μH
μᵣ = 1 + χ (relative permeability).
Hysteresis
The lag of magnetisation behind the magnetising field. The B-H curve forms a loop.
Retentivity: B remaining when H = 0. Coercivity: H needed to reduce B to zero.
Area of hysteresis loop = energy loss per cycle.
Soft magnetic materials (soft iron): low coercivity, low hysteresis loss -- used for electromagnets, transformers.
Hard magnetic materials (steel, Alnico): high coercivity, high retentivity -- used for permanent magnets.
Summary
Magnets behave as dipoles with properties analogous to electric dipoles. Earth has its own magnetic field characterized by declination, dip, and horizontal component. Magnetic materials are classified as diamagnetic, paramagnetic, or ferromagnetic based on their response to external fields. Hysteresis describes the lag in magnetisation and determines material applications.
Important Terms
- Magnetic Susceptibility (χ): Degree of magnetisation per unit magnetic intensity
- Curie Temperature: Temperature above which ferromagnetic becomes paramagnetic
- Retentivity: Residual magnetisation when external field is removed
- Coercivity: Reverse field needed to demagnetise completely
- Hysteresis: Dependence of magnetisation on history of applied field
Quick Revision
- M = NIA (current loop as magnetic dipole); τ = MB sin θ
- Earth: B_H = B cos I, B_V = B sin I, tan I = B_V/B_H
- Diamagnetic: χ < 0; Paramagnetic: χ > 0 (small); Ferromagnetic: χ >> 1
- B = μ₀(H + M); μᵣ = 1 + χ
- Curie's law (paramagnetic): χ ∝ 1/T
- Soft iron: electromagnets; Steel: permanent magnets