Ch 10: Magnetism | Exam Fusion Prep

🧲 Chapter At a Glance

Oersted

Discovered Magnetic Effect of Current (1820)

Faraday

Discovered EMI (1831)

Weber

SI Unit of Magnetic Flux

Fe₃O₄

Lodestone (Natural Magnet)

Magnet — attracts iron and its ores; always exists as dipole (N-S)
Magnetic effect of current — discovered by Oersted (1820)
Electromagnetic Induction — discovered by Faraday (1831)
Key rules: Biot-Savart Law · Ampere's Law · Lorentz Force · Fleming's Left & Right Hand Rules
3 magnetic material types: Diamagnetic · Paramagnetic · Ferromagnetic

📋 Key Formulae — Quick Look

dB = (μ₀/4π)·(IΔl sinθ/r²)Biot-Savart Law

∮ B·dl = μ₀IAmpere’s Law — Steady Currents

|F_B| = |q|vB sinθMagnetic part of Lorentz force

Φ = B·A cosθMagnetic Flux | Unit: Weber

🧲 Magnet — Basics

📘 Definition

Substances that have the property of attracting iron and its ores. Always exist as a dipole with North and South poles — isolated magnetic monopoles have not been experimentally observed.

Like Poles

Repulsion

Unlike Poles

Attraction

When suspended freely

N→ Geographic North

📂 Types of Magnets

Natural Magnet

Found in Nature

Minerals naturally possessing magnetism
Lodestone (Magnetite) = Fe₃O₄
Irregular shape, weak magnetic force

Artificial Magnet

Man-Made

Made from iron, steel, nickel combinations
Bar magnet
Electromagnet
Horse-shoe magnet
Magnetic compass

⚠️ Exam Trap — Natural Magnet

Lodestone = Magnetite = Fe₃O₄ (iron oxide)
When freely suspended, North pole of bar magnet points toward geographic North (actually Earth's magnetic south pole!)
No isolated magnetic monopole has been experimentally observed; cutting a bar magnet gives two dipoles

🧱 Classification of Materials Based on Magnetism

🔵 Diamagnetic

Caused by: Orbital motion of electrons
Magnetised in opposite direction to applied field
Weakly repelled by magnets

Examples:
Bismuth, Zinc, Gold, Copper, Silver, Diamond, Salt

🟡 Paramagnetic

Caused by: Spinning motion of electrons
Magnetised in the direction of field
Weakly attracted by magnets

Examples:
Sodium, Aluminium, Oxygen (chromium is antiferromagnetic near room temperature)

🔴 Ferromagnetic

Caused by: Domain formation
Strongly magnetised in direction of field
Strongly attracted by magnets

Examples:
Iron, Nickel, Cobalt, Steel

⚠️ Exam Trap — Magnetic Materials

Diamagnetic = repelled by magnet; magnetised OPPOSITE to field (Bismuth, Copper, Silver)
Paramagnetic = weakly attracted; magnetised in direction of field (Al, O₂; chromium is antiferromagnetic near room temperature)
Ferromagnetic = strongly attracted; domain formation (Iron, Nickel, Cobalt)
Silver & Copper = Diamagnetic (NOT ferromagnetic) — common trap!
Aluminium = Paramagnetic (NOT ferromagnetic)

🌐 Magnetic Field

📘 Definition

The region around a magnet or current-carrying conductor where magnetic effects are experienced.

⚡ Magnetic Effect of Electric Current

📘 Discovery

A magnetic field is produced around a current-carrying conductor. Discovered by Oersted (1820).

📐 Biot-Savart Law

dB = (μ₀/4π) · (IΔl sinθ / r²)Intensity of Magnetic Field | Unit: N/Am

μ₀/4π

10⁻⁷ N/A²

μ₀

Permeability of vacuum

Parameter	Relationship with element contribution dB
Current (I)	dB ∝ I (directly proportional)
Length (Δl)	dB ∝ Δl (directly proportional)
Distance (r)	dB ∝ 1/r² (inverse square)
Angle (θ)	dB ∝ sinθ

📏 Ampere's Law

∮ B · dl = μ₀ILine integral of B around a closed loop = μ₀ × enclosed current

μ₀ = Permeability of vacuum
dl = infinitesimal length element of the closed loop
Used to find B for symmetric current configurations (solenoid, toroid)

🧭 Rules for Direction of Magnetic Field

Rule A

Right-Hand Grip Rule

Right-hand grip rule: thumb along conventional current; curled fingers show the field around the wire

Rule B

Maxwell's Right Hand Rule

Thumb → Direction of current
Curled fingers → Direction of magnetic field around the conductor

Rule C

Maxwell's Cork Screw Rule

Viewed from above: upward current → anticlockwise field
Viewed from above: downward current → clockwise field

⚡ Lorentz Force

📘 Definition

Force experienced by a moving charged particle in a magnetic field.

F⃗_B = q(v⃗ × B⃗); |F_B| = |q|vB sinθMagnetic part of Lorentz force

F ∝ charge (q)
F ∝ velocity (v)
F ∝ magnetic field intensity (B)
F = 0 when θ = 0° or 180° (particle moves parallel to field)
F is maximum when θ = 90° (particle moves perpendicular to field)

⚠️ Exam Trap — Lorentz Force

A stationary charge in a magnetic field experiences NO force (|F_B| = |q|vB sinθ; v=0 → F=0). The charge must be moving to experience magnetic force.

🔌 Force on Current-Carrying Conductor

F = BIl sinθ (Newton)Force on conductor of length l carrying current I in field B

Direction: Perpendicular to both the magnetic field and the current
Maximum when current is perpendicular to B (θ = 90°)
Zero when current is parallel to B (θ = 0°)

✋ Fleming's Rules — Left & Right Hand

✊ Fleming's LEFT Hand Rule

Used for: Motor (Force on conductor)

Thumb

Force (F)

Forefinger

Field (B)

Middle Finger

Current (I)

🤚 Fleming's RIGHT Hand Rule

Used for: Generator (Induced Current)

Thumb

Motion of Conductor

Forefinger

Field (B)

Middle Finger

Induced Current

⚠️ Exam Trap — Left vs Right Hand

LEFT hand = MOTOR effect (current → force/motion) — FBI rule
RIGHT hand = GENERATOR / DYNAMO effect (motion → induced current)
Memory trick: Motor = Left | Generator = Right
Both rules use: Forefinger = Field (B), Middle = Current

〰️ Magnetic Field Lines

📘 Definition

Continuous imaginary lines representing the direction and strength of a magnetic field.

Direction: North → South pole (outside the magnet)
Form closed curves (unlike electric field lines)
Non-intersecting (never cross each other)
Parallel and equally spaced in a uniform field
Magnetic field = zero at neutral point
Closer lines = stronger field; farther lines = weaker field

⚠️ Exam Trap — Magnetic vs Electric Field Lines

Property	Electric Field Lines	Magnetic Field Lines
Direction	+ to −	N to S (outside magnet)
Closed loops?	No	Yes
Intersect?	No	No
Originate/end	On charges	No start/end (continuous)

🔌 Electromagnet

📘 Definition

A magnet obtained by winding wire around an iron core and passing electric current through it. Becomes magnetic only when current flows.

Core material: Soft iron (easily magnetised and demagnetised)
Magnetic strength increases with: more turns of wire, more current, better core material
Applications: Electric bells, cranes for lifting scrap iron, MRI machines, electric motors
Advantage over permanent magnets: strength can be controlled

🌀 Magnetic Flux (Φ)

📘 Definition

Magnetic flux is Φ = ∫ B⃗·dA⃗; for a uniform field through a planar area, Φ = BA cosθ. Field-line count is a visual analogy.

Φ = B · A cosθMagnetic Flux | B = field, A = area, θ = angle between B and normal to surface

SI Unit

Weber (Wb)

Other SI

N·m/A

CGS Unit

Maxwell

Conversion

1 Wb = 10⁸ Maxwell

⚠️ Exam Trap — Magnetic Flux

Flux is maximum when B is perpendicular to surface (θ = 0°, cosθ = 1)
Flux is zero when B is parallel to surface (θ = 90°, cosθ = 0)
Unit: Weber (SI); Maxwell (CGS) | 1 Wb = 10⁸ Maxwell

⚙️ Electromagnetic Induction (EMI)

📘 Definition

Phenomenon of generation of EMF and induced current in a conductor due to changing magnetic flux.

Discoverer

Michael Faraday

Year

1831

EMF is induced only when magnetic flux is changing
Key principle: A changing magnetic field creates an electric field

📘 Applications of EMI

Dynamo / Generator — converts mechanical energy to electrical
Transformer — changes AC voltage levels
Induction cooktop — induced currents heat a suitable pan
Induction cooktop, wireless charging

Direction of Induced Current

Fleming's Right Hand Rule

Thumb

Motion of Conductor

Forefinger

Magnetic Field (B)

Middle Finger

Induced Current

⚠️ Exam Trap — EMI

EMI requires changing flux — a stationary coil with unchanging flux linkage has no induced EMF
Faraday discovered EMI in 1831 (NOT Oersted — Oersted discovered magnetic effect of current in 1820)
Generator works on EMI; Motor works on magnetic force on current (reverse of EMI)
Right hand rule = Generator; Left hand rule = Motor

🎯 High-Yield Exam Points

Natural magnet = Lodestone = Magnetite = Fe₃O₄
Like poles = Repulsion; Unlike poles = Attraction
Ordinary magnets have north and south poles; isolated monopoles have not been experimentally observed
Diamagnetic: Bismuth, Copper, Silver, Gold (repelled, opposite magnetisation)
Paramagnetic: Aluminium and oxygen (weakly attracted); chromium is antiferromagnetic near room temperature
Ferromagnetic: Iron, Nickel, Cobalt (strongly attracted, domains)
Magnetic effect of current: Oersted (1820)
Biot-Savart: dB ∝ I, dB ∝ Δl, dB ∝ 1/r², dB ∝ sinθ
μ₀/4π = 10⁻⁷ N/A²
Lorentz force: |F_B| = |q|vB sinθ (zero for stationary charge)
Force on conductor: F = BIl sinθ
Left Hand Rule → Motor (Force); Right Hand Rule → Generator (Induced current)
Magnetic field lines: N→S, closed curves, non-intersecting
Electromagnetic Induction: Faraday (1831)
Magnetic Flux unit: Weber (SI) | 1 Wb = 10⁸ Maxwell
Φ = B·A cosθ; max when θ = 0°, zero when θ = 90°
Applications of EMI: Dynamo, transformer, induction cooktop
Cork screw rule: Viewed from above: current up → anticlockwise B; current down → clockwise B

📋 Formula Quick Reference

dB = (μ₀/4π)·IΔl sinθ/r²Biot-Savart Law | μ₀/4π = 10⁻⁷

∮ B·dl = μ₀IAmpere’s Law — Steady Currents

|F_B| = |q|vB sinθMagnetic part of Lorentz force

F = BIl sinθForce on Current Conductor

Φ = B·A cosθMagnetic Flux (Weber)

⚠️ Most Common Exam Traps

Silver & Copper = Diamagnetic (NOT conductors of magnetism)
Aluminium = Paramagnetic (NOT ferromagnetic)
Oersted (1820) ≠ Faraday (1831) — different discoveries
Stationary charge: magnetic force is zero; an electric field can still exert force
Left hand = Motor; Right hand = Generator
Magnetic field lines form closed loops (electric field lines do NOT)
1 Weber = 10⁸ Maxwell (not 10⁶ or 10¹⁰)
EMI requires changing flux, not just a magnetic field
Lodestone = Fe₃O₄ (iron(II,III) oxide — NOT FeO or Fe₂O₃)

🧲 Chapter 10: Magnetism