Magnetism

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Magnetism is a fundamental topic in physics that deals with magnetic materials, magnetic fields, and electromagnetic phenomena. In CUET UG Physics, this chapter covers Earth’s magnetism, magnetic properties of materials, and the origin of magnetism at atomic level.

Key Definitions:

• Magnetic Field (B): Region around a magnet where magnetic force acts
• Magnetic Flux (Φ): Total magnetic field passing through a surface (Φ = B·A·cosθ, Weber)
• Magnetic Moment (m): Measure of magnetic strength (A·m²)
• Magnetisation (M): Magnetic moment per unit volume (A/m)

Earth’s Magnetic Field:

• Earth’s magnetic field is like a dipole with magnetic south pole near geographic north
• Horizontal component: $B_H = B \cos\theta$
• Vertical component: $B_V = B \sin\theta$
• Angle of dip (δ): $\tan^{-1}(B_V/B_H)$
• At magnetic equator: δ = 0°
• At magnetic poles: δ = ±90°

Magnetic Materials:

Type	Properties	Examples
Diamagnetic	Weak repulsion, no permanent moment	Bismuth, Copper, Water
Paramagnetic	Weak attraction, aligned by field	Aluminium, Oxygen, Manganese
Ferromagnetic	Strong attraction, permanent magnets	Iron, Cobalt, Nickel

Curie’s Law: For paramagnetic materials, χ = C/T where C is Curie constant and T is temperature. Above Curie temperature (T_C), ferromagnets become paramagnetic.

⚡ CUET Exam Tips:

• Soft iron has high permeability — used for temporary electromagnets
• Steel has high coercivity — used for permanent magnets
• Magnetism is due to movement of electrons (orbital and spin)
• Earth’s magnetic field protects us from solar wind

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Understanding Magnetic Properties:

Hysteresis Loop: When a ferromagnetic material is magnetised and demagnetised cyclically, the B-H curve shows hysteresis (lag of B behind H).

• Retentivity: Magnetisation remaining after removing external field (point where curve cuts B-axis)
• Coercivity: Field needed to reduce magnetisation to zero (point where curve cuts H-axis)
• Hysteresis Loss: Energy lost per unit volume per cycle = Area of hysteresis loop

Soft vs Hard Magnetic Materials:

Property	Soft Iron	Steel
Retentivity	Low	High
Coercivity	Low	High
Hysteresis loss	Low	High
Uses	Electromagnets, transformers	Permanent magnets

Magnetic Screening (Faraday Cage for Magnetism): A ferromagnetic shell shields interior from external magnetic fields. The magnetic field lines are forced to pass through the shell rather than enter the cavity.

Origin of Magnetism:

Electronic Magnetic Moment:

• Orbital magnetic moment: Due to electron revolution around nucleus
• Spin magnetic moment: Intrinsic property of electrons (like spinning top)
• Bohr magneton (μ_B): $\mu_B = \frac{eh}{4\pi m} = 9.27 \times 10^{-24}$ A·m²

Domain Theory of Ferromagnetism:

• Ferromagnetic materials have small regions called domains
• Each domain has parallel alignment of magnetic moments
• In unmagnetised state, domains point in random directions
• On applying external field, domains align in field direction
• Above Curie temperature, thermal agitation destroys domain alignment

Gauss’s Law for Magnetism: The net magnetic flux through any closed surface is zero: $\oint \mathbf{B} \cdot d\mathbf{A} = 0$ (This implies magnetic monopoles don’t exist — every magnet has north and south pole)

Magnetisation and Susceptibility:

$$M = \frac{\text{magnetic moment}}{\text{volume}} \quad (\text{A/m})$$

$$\chi = \frac{M}{H} \quad \text{(magnetic susceptibility)}$$

$$\mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M}) = \mu_0\mu_r\mathbf{H}$$

$$\mu_r = 1 + \chi$$

⚠️ CUET Common Mistakes:

1. Confusing magnetic pole names (geographic north ≠ magnetic north)
2. Forgetting that magnetic flux is scalar but flux density is vector
3. Not understanding hysteresis loop correctly
4. Mixing up diamagnetic, paramagnetic, and ferromagnetic properties

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage with derivations, applications, and previous year CUET patterns.

Magnetic Circuits:

Magnetic circuits follow laws analogous to electric circuits:

Electric Circuit	Magnetic Circuit
EMF (V)	MMF (NI)
Current (I)	Flux (Φ)
Resistance (R)	Reluctance (S)
Ohm’s Law: V = IR	Ohm’s Law: Φ = MMF/S

$$MMF = \ NI \quad \text{(Ampere-turns)}$$

$$S = \frac{l}{\mu_0\mu_r A} \quad \text{(Reluctance)}$$

$$\Phi = \frac{NI}{S}$$

Magnetisation Curves:

B-H Curve for Different Materials:

• Initial magnetisation curve rises steeply then saturates
• Hysteresis loop area determines energy loss
• Smaller loop = less energy loss = better soft magnetic material

Force on Moving Charge in Magnetic Field:

$$\mathbf{F} = q(\mathbf{v} \times \mathbf{B})$$

• Magnitude: $F = qvB\sin\theta$
• Direction: Given by Fleming’s left-hand rule
• Unit: Newton (N)

Force on Current-Carrying Conductor:

$$\mathbf{F} = I(\mathbf{L} \times \mathbf{B})$$

• For straight wire in uniform field: $F = BIL\sin\theta$
• For coil: Torque $\tau = NIAB\sin\theta$

Cyclotron Motion:

When a charged particle enters perpendicular to uniform B:

• Circular path with radius: $r = \frac{mv}{qB}$
• Time period: $T = \frac{2\pi m}{qB}$ (independent of velocity!)
• Angular frequency: $\omega = \frac{qB}{m}$

Applications of Magnetism:

Electric Motor: Converts electrical energy to mechanical energy using magnetic forces on current-carrying conductors.

Generator: Converts mechanical energy to electrical energy using electromagnetic induction.

Magnetic Resonance Imaging (MRI): Uses nuclear magnetic resonance to image internal body structures.

Maglev Trains: Use magnetic levitation for frictionless movement.

Previous Year CUET Patterns:

CUET 2022: The magnetic moment of an electron due to orbital motion is given by: a) $\mu_B$ b) $\frac{eh}{4\pi m}$ c) $\frac{eh}{2\pi m}$ d) $\frac{eh}{4\pi m^2}$ Answer: b) $\frac{eh}{4\pi m}$ (Bohr magneton)

CUET 2022: The materials which are weakly attracted by magnetic field are called: a) Ferromagnetic b) Paramagnetic c) Diamagnetic d) Non-magnetic Answer: b) Paramagnetic

CUET 2023: The ratio of magnetic field at the centre of a current-carrying coil to that at its axis is: a) $\sqrt{3}$ b) $\sqrt{2}$ c) $1$ d) $\frac{1}{\sqrt{3}}$ Answer: a) $\sqrt{3}$ (For a circular coil, field at centre is $\frac{\mu_0 I}{2r}$ perpendicular to plane, while at a point on axis at distance x, it’s $\frac{\mu_0 I r^2}{2(r^2+x^2)^{3/2}$. At x=r, ratio = $\sqrt{3}$.)

CUET 2023: Hysteresis loss in a magnetic material does NOT depend on: a) Frequency of magnetisation cycle b) Volume of material c) Shape of material d) Area of hysteresis loop Answer: c) Shape of material — Hysteresis loss depends on material properties and volume, not shape.

Advanced Concepts:

Curie-Weiss Law: For paramagnets above Curie temperature: $\chi = \frac{C}{T - T_C}$

Neel Temperature: For antiferromagnetic materials, above this temperature they become paramagnetic.

Superparamagnetism: When ferromagnetic nanoparticles behave like paramagnets due to thermal effects overcoming anisotropy barriers.

GMeter vs Gaussmeter: Device to measure magnetic field strength using Hall effect.

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