Magnetism

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Magnetism — Key Facts

Earth’s Magnetic Field:

Earth behaves as a magnetic dipole with magnetic south pole near geographic north. The horizontal component of Earth’s field: $$B_H = B \cos\theta$$

where θ = angle of dip (angle between Earth’s field and horizontal)

Vertical component: $B_V = B \sin\theta = B_H \tan\theta$

At magnetic equator: θ = 0°, so B_V = 0 At magnetic poles: θ = 90°, so B_H = 0

Magnetic Materials:

Type	Behaviour	Examples
Diamagnetic	Weakly repelled by magnets; no permanent moment	Bismuth, copper, water
Paramagnetic	Weakly attracted; aligned by field	Aluminium, oxygen, manganese
Ferromagnetic	Strongly attracted; permanent magnets below T_C	Iron, nickel, cobalt

Curie Law (Paramagnetic): $$\chi = \frac{C}{T}$$

where χ = magnetic susceptibility, C = Curie constant, T = temperature

Above Curie temperature (T_C), ferromagnetic materials become paramagnetic.

⚡ JEE Exam Tip: Soft iron has high permeability and low coercivity — good for electromagnets (can be magnetised/demagnetised easily). Steel has high coercivity — good for permanent magnets (hard to demagnetise).

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding…

Hysteresis:

When a ferromagnetic material undergoes a magnetisation-demagnetisation cycle, the B-H curve shows hysteresis (lag of B behind H).

Key properties:

• Remanence (Retentivity): B remaining when H = 0 (gives permanent magnetism)
• Coercivity: H needed to reduce B to zero (resistance to demagnetisation)
• Hysteresis loss: Area inside B-H loop = energy lost per unit volume per cycle

Soft iron: narrow hysteresis loop → low coercivity → low energy loss → good for transformers. Steel: wide hysteresis loop → high coercivity → high energy loss → good for permanent magnets.

Magnetic Screening (Faraday Cage for Magnetism):

A ferromagnetic shell shields its interior from external magnetic fields. The field lines are diverted through the ferromagnetic material.

This is why sensitive equipment is sometimes housed in mu-metal (high permeability alloy) enclosures.

Magnetic Materials at High Frequency:

At high frequencies, ferromagnetic materials show eddy current losses. Laminations (thin insulated sheets) are used to reduce eddy currents in transformer cores.

⚡ JEE Exam Tip: The BH curve is non-linear for ferromagnets. The permeability μ = B/H is not constant — it varies with H. At magnetic saturation, μ drops significantly.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Origin of Magnetism:

All magnetic effects arise from electric charges in motion:

1. Orbital magnetic moment: electron revolving around nucleus (like current loop)
2. Spin magnetic moment: intrinsic property of electron (quantum mechanical)

Bohr magneton: $\mu_B = \frac{e\hbar}{2m_e} = 9.27 \times 10^{-24}$ J/T

Total magnetic moment of electron: $\vec{\mu} = -\frac{e}{2m}(\vec{L} + 2\vec{S})$ (Landé g-factor: $g = 1 + \frac{J(J+1) + S(S+1) - L(L+1)}{2J(J+1)}$)

Domain Theory of Ferromagnetism:

Below Curie temperature, ferromagnetic materials consist of magnetic domains:

• Within each domain, all atomic magnetic moments are aligned
• Different domains have different directions
• An external field causes domains aligned with the field to grow at expense of others
• Above T_C, thermal energy destroys domain alignment → material becomes paramagnetic

Magnetisation and Magnetic Quantities:

Magnetisation: $\vec{M} = \frac{\text{magnetic moment}}{\text{volume}}$ (unit: A/m)

Magnetic intensity: $\vec{H}$

Relation: $\vec{B} = \mu_0(\vec{H} + \vec{M}) = \mu_0\mu_r\vec{H}$

Magnetic susceptibility: $\chi_m = \frac{M}{H}$

For vacuum: χ = 0; for diamagnetic: χ < 0; for paramagnetic: χ > 0; for ferromagnetic: χ >> 0

Magnetic Circuits:

Similar to electric circuits, with magnetic flux Φ playing the role of current:

Electric Circuit	Magnetic Circuit
EMF (ε)	MMF (NI)
Current (I)	Flux (Φ)
Resistance (R)	Reluctance (R = l/μA)
$I = \varepsilon/R$	$\Phi = MMF/R$

Ohm’s law for magnetic circuits: $\mathcal{F} = \Phi \cdot \mathcal{R}$

Hysteresis Loss Calculation:

Hysteresis loss per unit volume per second: $P_h = \eta B_{max}^n f$ where η = Steinmetz constant, n ≈ 1.6, f = frequency

Eddy current loss: $P_e = \eta_e B_{max}^2 f^2 t^2$ (where t = thickness of laminations)

⚡ JEE Advanced 2022 Analysis: Hysteresis loops, energy in magnetic field, and magnetic circuits appeared in recent JEE Advanced. Remember: for magnetic circuits with air gaps, the reluctance of the air gap dominates (μ_air << μ_iron).

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