Class 12 · Chapter 5

Magnetism & Matter

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Magnetism & Matter Formula Sheet

5 formulas across 2 topics in Magnetism & Matter.

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Updated 2026-07-05 · v1.0.0

Bar Magnet as a Dipole

A bar magnet is a magnetic dipole — every electrostatic dipole result carries over with p → m and 1/4πε₀ → μ₀/4π.

Axial: B = (μ₀/4π) 2m/r³; Equatorial: B = (μ₀/4π) m/r³

Field of a bar magnet (short dipole)

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
m	magnetic dipole moment	A·m²	[AL²]
r	distance from the magnet's centre	m	[L]
μ₀	permeability of free space	T·m/A	[MLT⁻²A⁻²]

Valid when

Short-dipole approximation r ≫ magnet length
Axial field is twice the equatorial at equal distance

Common mistakes

Direct analogy to the electric dipole: swap p → m and 1/4πε₀ → μ₀/4π and the formulas match exactly

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τ = mB sinθ; U = −mB cosθ

Torque and energy of a magnet in a field

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
θ	angle between m and B	rad (or °)	[M⁰L⁰T⁰]
B	external magnetic field	T	[MT⁻²A⁻¹]

Valid when

Stable equilibrium at θ = 0 (aligned with B), unstable at θ = 180°

Common mistakes

Work to rotate from θ₁ to θ₂: W = mB(cosθ₁ − cosθ₂); flipping a magnet end-for-end costs 2mB

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T = 2π √(I/(mB))

Oscillation of a magnet in a field

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Restoring torque −mB sinθ ≈ −mBθ for small angles (angular SHM)

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
I	moment of inertia of the magnet	kg·m²	[ML²]
m	magnetic moment	A·m²	[AL²]
B	field the magnet oscillates in	T	[MT⁻²A⁻¹]

Valid when

Small-angle angular SHM — the magnetic analogue of a pendulum
Used in vibration magnetometers to compare field strengths

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Worth remembering

Isolated magnetic poles (monopoles) have never been found — cutting a magnet just makes two smaller dipoles
Gauss's law for magnetism: ∮B·dA = 0 always — net magnetic flux through any closed surface is zero

Magnetic Materials & Properties

Materials respond to a field through their susceptibility. The sign and size of χ sort every substance into dia-, para-, or ferromagnetic.

B = μ₀(H + M); M = χH; μ(r) = 1 + χ

Magnetising field, magnetisation & permeability

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
H	magnetising field intensity	A/m	[L⁻¹A]
M	magnetisation (dipole moment per volume)	A/m	[L⁻¹A]
χ	magnetic susceptibility	dimensionless	[M⁰L⁰T⁰]
μ(r)	relative permeability	dimensionless	[M⁰L⁰T⁰]

Valid when

B is the net field; H is the applied/free-current part; M is the material's response

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Dia: χ small negative; Para: χ small positive, χ ∝ 1/T; Ferro: χ large positive

Classification of magnetic materials

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
χ	magnetic susceptibility	dimensionless	[M⁰L⁰T⁰]
T	absolute temperature	K	[Θ]

Valid when

Diamagnetic: χ ≈ −10⁻⁵, repelled, moves to weak-field region (e.g. bismuth, water)
Paramagnetic: χ small +, Curie law χ = C/T (e.g. aluminium)
Ferromagnetic: χ ≫ 1, becomes paramagnetic above the Curie temperature

Common mistakes

Diamagnetism is the only material property INDEPENDENT of temperature; para- and ferro- weaken as T rises

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Worth remembering

Curie temperature: above it a ferromagnet loses spontaneous magnetisation and turns paramagnetic (iron ≈ 1043 K)
Hysteresis loop area = energy lost per cycle; soft iron (thin loop) for transformers, steel (fat loop) for permanent magnets

NEET and Boards lean heavily on the dia/para/ferro classification and Curie law; JEE Main occasionally computes with B = μ₀(H + M). Note: this chapter is not in the JEE Advanced syllabus.

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Previous chapter4. Moving Charges & Magnetism Next chapter 6. Electromagnetic Induction

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