Magnetism and Matter

magnetism part 2

Use: Notes + Revision

Magnetic Dipole

Basics

M = m × l

m = pole strength
l = distance between poles
Direction: S → N
Unit: A·m²

Torque & Potential Energy

Dipole

τ = M B sinθ

U = − M B cosθ

Stable: θ = 0°
Unstable: θ = 180°
Work done: change in potential energy

Magnetic Field Lines

Properties

Always form closed loops
Outside magnet: N → S
Inside magnet: S → N
Never intersect
Density ∝ field strength

Magnetic Monopole

Fact

Magnetic monopoles do not exist
Smallest unit = dipole
Cutting magnet → always 2 poles

Gauss Law (Magnetism)

Flux

∮ B·dS = 0

Net magnetic flux = 0
No source or sink of magnetic field

Resultant Dipole Moment

Vector

Mnet = √(M₁² + M₂² + 2M₁M₂cosθ)

Depends on angle between dipoles

Cutting of Magnet

Cases

Lengthwise: m same, l decreases
Transverse: l same, m decreases
Dipole moment changes accordingly

Earth’s Magnetism

Elements

Declination: angle between geographic & magnetic meridian
Dip (δ): angle between field & horizontal
tanδ = Bv / Bh

Angle of Dip

Facts

Maximum at poles
Minimum (0°) at equator
Declination higher near poles

Magnetic Materials

Types

Diamagnetic: weakly repelled, no permanent dipole
Paramagnetic: weakly attracted, follows Curie law
Ferromagnetic: strongly attracted, domains align
At high temperature → ferromagnetic becomes paramagnetic

Hysteresis Curve

B-H

Area = energy loss (heat)
Loop shows magnetisation history
Important for materials selection

Magnetic Quantities

Relations

B = μ₀(H + M)
Magnetisation: M
Magnetic field intensity: H
Susceptibility: χ
μr = 1 + χ

Magnet Types

Applications

Permanent magnets: high retentivity & coercivity (steel)
Soft magnets: low coercivity, high permeability (soft iron)
Soft iron used in electromagnets
Applications: electric bells, cranes, speakers