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Physics  ·  NDA

Magnetism

📖 Chapter PN06  ·  NDA Class 11–12 Level

Magnetism is the study of forces produced by magnets and electric currents, and of Earth's own vast magnetic field. For NDA, this chapter focuses on the properties of magnets, distinguishing natural from artificial and permanent from electromagnets, and deeply understanding Earth's magnetism — including magnetic elements and the mariner's compass used in navigation. The chapter is highly applied and connects directly to defence technology and navigation.

📌 What to expect in NDA (based on 2022–2025 pattern):
(1) Properties of magnets — poles, attraction, repulsion, magnetic field lines;
(2) Types of magnets — natural (lodestone), artificial (bar, horseshoe), electromagnets;
(3) Methods of magnetisation and demagnetisation;
(4) Magnetic materials — diamagnetic, paramagnetic, ferromagnetic;
(5) Earth's magnetism — geographic vs magnetic poles, magnetic declination, dip (inclination);
(6) Mariner's compass — working principle, magnetic north vs true north;
(7) Electromagnets — solenoid, factors affecting strength, applications in defence.

Topics at a Glance

① Properties of Magnets
Poles, attraction, repulsion, field lines, keepers
② Types of Magnets
Natural, artificial, permanent, electromagnets
③ Magnetic Materials
Diamagnetic, paramagnetic, ferromagnetic
④ Earth's Magnetism
Magnetic poles, declination, dip, horizontal component
⑤ Mariner's Compass
Magnetic north, true north, compass bearings
⑥ Electromagnets
Solenoid, current, core material, applications

1. Properties of Magnets

1.1
Fundamental Properties & Magnetic Field Lines
What every magnet does — attraction, repulsion, and the invisible field around it

A magnet is any object that produces a magnetic field and attracts ferromagnetic materials. Every magnet has two poles — North (N) and South (S) — where the magnetic force is strongest. These poles cannot be separated — breaking a magnet always creates two new complete magnets, each with both poles.

📍 Fundamental Laws

  • Like poles repel: N–N and S–S repel
  • Unlike poles attract: N–S attract
  • Repulsion is the sure test of magnetism
  • Magnetic poles always exist in pairs (dipole)
  • Isolated magnetic pole (monopole) does not exist
  • Magnetic force acts through non-magnetic materials

📊 Magnetic Field Lines

  • Imaginary lines showing direction of magnetic force
  • Direction: from North pole to South pole outside magnet
  • Inside magnet: S to N (continuous closed loops)
  • Never intersect each other
  • Closer lines = stronger field
  • Tangent at any point = direction of B at that point

🔸 Key Properties of Magnets

  • Attractive property: attracts iron, nickel, cobalt
  • Directive property: freely suspended magnet points N-S
  • Repulsive property: like poles repel (true test of magnetism)
  • Inductive property: can magnetise nearby iron
  • Poles nearest to ends but not exactly at ends
S N Bar Magnet Field lines exit from N Field lines enter at S Magnetic Field Lines of a Bar Magnet Lines are continuous closed loops (inside magnet: S → N). Never cross each other. Denser near poles = stronger field.
Fig. 1 — Magnetic field lines of a bar magnet. Outside the magnet: N → S. Inside the magnet: S → N (continuous loops). Field is strongest (densest lines) near the poles.
⚡ Coulomb's Law of Magnetic Force & Magnetic Dipole
Coulomb's Law (between magnetic poles): F = μ₀/4π × (m₁ × m₂) / r² m = pole strength (A·m), r = distance between poles μ₀ = 4π × 10⁻⁷ T·m/A (permeability of free space) Magnetic Dipole Moment (M): M = m × 2l (pole strength × magnetic length) M = I × A (for current loop: current × area) Unit: A·m² Dimension: IL² Torque on dipole in uniform field: τ = MB sinθ → τ = M × B (vector form) Equilibrium: θ = 0° (stable) or 180° (unstable) Potential energy of dipole: U = −MB cosθ = −M·B
A bar magnet behaves as a magnetic dipole. The magnetic length (2l) is slightly less than the physical length — poles are not exactly at the geometric ends but approximately 5/6th of the half-length from centre.
💡 Repulsion is the SURE test of magnetism. An unmagnetised iron rod will be attracted to either pole of a magnet (magnetic induction). So attraction alone cannot confirm whether the object is a magnet. Only if a pole repels the rod is it confirmed to be a magnet — because like poles repel, and repulsion cannot occur due to mere induction.
📝 TOPIC-WISE PYQ
Properties of Magnets — NDA Pattern Questions
Q1. A bar magnet is cut into two equal halves perpendicular to its length. What happens to the pole strength and magnetic moment?
  • (a) Both halved    (b) Pole strength same, moment halved    (c) Both doubled    (d) Pole strength halved, moment same
Answer: (b) Pole strength same, moment halved
Cutting perpendicular to length: each half has the same pole strength m (cutting doesn't remove poles). But the magnetic length l becomes l/2. Magnetic moment M = m × 2l → M' = m × l = M/2. Pole strength unchanged; magnetic moment is halved.
Q2. The sure test to identify a magnet from an unmagnetised iron bar is:
  • (a) Attraction    (b) Repulsion    (c) Weight comparison    (d) Colour
Answer: (b) Repulsion
An iron bar is attracted to both poles of a magnet due to magnetic induction — attraction alone cannot distinguish a magnet from iron. Only a magnet can repel another magnet (like pole repels like pole). Repulsion is the sure test of magnetism.
Q3. Magnetic field lines of a bar magnet:
  • (a) Start and end at poles    (b) Are open curves outside only    (c) Form continuous closed loops    (d) Can intersect at neutral points
Answer: (c) Form continuous closed loops
Magnetic field lines are always closed loops — they go from N to S outside the magnet and from S to N inside. They never start or end at a point (no magnetic monopole) and never intersect each other.

2. Types of Magnets

2.1
Natural, Artificial & Electromagnets
From lodestone to MRI machines — the spectrum of magnetic devices
TypeDescriptionExamplesAdvantage / Use
Natural Magnet Found naturally in earth; magnetic property due to aligned iron oxide (Fe₃O₄) Lodestone (magnetite) First magnets known to humans; used by ancient sailors
Artificial Permanent Magnet Made by magnetising steel or alloys; retains magnetism indefinitely Bar magnet, horseshoe magnet, compass needle Predictable, portable, no power needed
Electromagnet Magnetism produced by electric current through a coil; temporary Solenoid with iron core, relay switch, crane magnet Controllable strength; can be switched on/off; very strong
Temporary Magnet Soft iron core — magnetised only while current flows Iron core of a doorbell, electric bell Quickly loses magnetism when current stops
2.2
Methods of Magnetisation & Demagnetisation
How magnets are made and destroyed

🔧 Methods of Magnetisation

  • Single touch method: stroke iron bar with a magnet (one direction)
  • Double touch / divided touch: stroke from centre outward with both poles
  • Electrical method: pass current through solenoid with iron bar inside
  • Electrical method → strongest and most reliable magnets
  • Hammering iron bar while aligned N-S also magnetises (weakly)

🔥 Methods of Demagnetisation

  • Heating: heating beyond Curie temperature destroys magnetism
  • Hammering: rough mechanical vibration disturbs domain alignment
  • AC demagnetisation: place in alternating magnetic field then slowly withdraw
  • Dropping repeatedly also causes gradual loss of magnetism
  • Curie temperature: Fe ≈ 770°C, Ni ≈ 358°C, Co ≈ 1115°C
💡 Keepers — preserving permanent magnets: A horseshoe magnet is stored with a soft iron bar called a keeper placed across its poles. The keeper completes the magnetic circuit, reducing the demagnetising effect of the magnet's own stray field. Bar magnets are stored in pairs with opposite poles adjacent, with soft iron bars at both ends — this completes the circuit and prevents self-demagnetisation.
📝 TOPIC-WISE PYQ
Types of Magnets & Magnetisation — NDA Pattern Questions
Q1. Which of the following is used as the core of an electromagnet and why?
  • (a) Steel — high retentivity    (b) Soft iron — high permeability and low retentivity    (c) Copper — good conductor    (d) Aluminium — low density
Answer: (b) Soft iron — high permeability and low retentivity
Soft iron has high permeability (gets strongly magnetised) and low retentivity (loses magnetism quickly when current stops). This makes it ideal for electromagnets that must be switched on and off. Steel has high retentivity — useful for permanent magnets, not electromagnets.
Q2. A magnet loses its magnetism when:
  • (a) Kept in air    (b) Heated above Curie temperature    (c) Placed near a weaker magnet    (d) Used to attract iron filings
Answer: (b) Heated above Curie temperature
Above the Curie temperature, thermal energy overcomes the coupling between magnetic domains — domains become randomly oriented and net magnetisation becomes zero. For iron, Curie temp ≈ 770°C. Hammering and AC demagnetisation also work but heating is most definitive.
Q3. Which is the most reliable and strongest method of magnetising a steel bar?
  • (a) Single touch method    (b) Double touch method    (c) Electrical method (solenoid)    (d) Storing near another magnet
Answer: (c) Electrical method (solenoid)
Passing DC current through a solenoid with the steel bar inside produces the strongest and most uniform magnetisation. The direction and strength are precisely controllable. Industrial magnets and all modern artificial magnets are made this way.
🤔 TRICKY QUESTIONS
Magnet Types — Conceptual Traps
T1. A bar magnet is broken into two pieces. Does each piece have only one pole?
No — each piece becomes a complete magnet with both N and S poles.
Magnetism arises from aligned magnetic domains throughout the material, not just at the ends. When you break a magnet, new poles form at the break point — each half immediately has both a north and south pole. This demonstrates that magnetic monopoles do not exist. Breaking a magnet never isolates a single pole, no matter how many times you cut it.
T2. Why is steel preferred over soft iron for making permanent magnets, but soft iron preferred for electromagnets?
It comes down to retentivity vs permeability.
Steel: high retentivity (holds magnetism after field removed) + high coercivity (hard to demagnetise) → ideal for permanent magnets.
Soft iron: high permeability (gets strongly magnetised by weak field) + low retentivity (loses magnetism when field removed) + low coercivity → ideal for electromagnets that must switch on/off rapidly. MRI machines use superconducting electromagnets; electric bells and relays use soft iron cores.

3. Magnetic Materials

3.1
Diamagnetic, Paramagnetic & Ferromagnetic Materials
How different materials respond to an external magnetic field

Not all materials respond to magnetic fields the same way. Materials are classified into three categories based on how their atoms respond to an applied field and how strongly they are attracted or repelled.

PropertyDiamagneticParamagneticFerromagnetic
Response to fieldWeakly repelledWeakly attractedStrongly attracted
Relative permeability (μᵣ)Slightly < 1Slightly > 1Very high (thousands)
Susceptibility (χ)Small negativeSmall positiveVery large positive
Effect of temperatureUnaffectedDecreases (Curie law)Decreases; zero above Curie temp
DomainsNo domainsNo domainsMagnetic domains exist
ExamplesBismuth, copper, water, gold, silver, leadAluminium, platinum, manganese, oxygen (gas)Iron, cobalt, nickel, steel, gadolinium
ApplicationMRI contrast; frictionless bearingsLiquid O₂ in MRI, paramagnetic sensorsElectromagnets, transformers, motors
⚠ NDA Exam Trap — Aluminium is paramagnetic, NOT diamagnetic or ferromagnetic. Students often classify aluminium as non-magnetic and confuse it with diamagnetic. Aluminium is weakly attracted to magnets (paramagnetic). Bismuth and copper are diamagnetic (weakly repelled). Only iron, nickel, cobalt (and alloys) are ferromagnetic (strongly attracted). Liquid oxygen is paramagnetic — it clings to magnets — a surprising and frequently tested NDA fact.

4. Earth's Magnetism

4.1
Earth as a Giant Magnet — Magnetic Field & Poles
Understanding the invisible shield that protects Earth and guides navigators

Earth behaves as if a giant bar magnet were placed inside it, tilted at about 11.5° from the geographic axis. The source of Earth's magnetic field is the movement of molten iron and nickel in Earth's outer core — called the dynamo effect. This field extends far into space, forming the magnetosphere which deflects harmful solar wind particles.

🌎 Geographic vs Magnetic Poles

  • Geographic North Pole: true north; axis of rotation
  • Magnetic North Pole: where compass needle points; currently near geographic north in northern Canada (~80°N, 110°W)
  • Earth's magnetic S pole is near geographic N pole (compass N points to it because opposite poles attract)
  • Magnetic poles shift slowly (secular variation)
  • Poles are inclined ~11.5° from geographic poles

🏭 Earth's Magnetic Field Direction

  • At geographic north: field points downward into Earth
  • At equator: field is horizontal, pointing north
  • At geographic south: field points upward out of Earth
  • Intensity: ~25–65 μT at Earth's surface
  • Field reverses every few hundred thousand years (geomagnetic reversal)
⚡ Magnetic Elements of Earth — Three Key Parameters
1. MAGNETIC DECLINATION (α or D): Angle between magnetic meridian and geographic meridian at a point = Angle between true north and magnetic north East declination (+): magnetic N is east of true N West declination (−): magnetic N is west of true N India: mostly has east declination 2. MAGNETIC DIP / INCLINATION (δ or I): Angle made by Earth's total magnetic field (B) with the horizontal At magnetic poles: δ = 90° (field is vertical) At magnetic equator: δ = 0° (field is horizontal) At other latitudes: 0° < δ < 90° Measured by dip needle (dip circle) 3. HORIZONTAL COMPONENT (H): H = B cosδ (horizontal component of Earth's field) V = B sinδ (vertical component of Earth's field) tan δ = V/H B = √(H² + V²) (total field intensity) At equator: H = B (maximum), V = 0 At poles: H = 0, V = B (maximum)
These three quantities — declination, dip, and horizontal component — are called the magnetic elements of Earth. Together they completely describe Earth's magnetic field at any location. Navigation, surveying, and defence operations depend on knowing these.
Earth Geographic N Geographic S Magnetic S pole Magnetic N pole α (declination) Observer Horizontal B (total field) H = B cosδ V = B sinδ δ (dip) Magnetic Elements α = Declination Geographic N vs Magnetic N δ = Dip / Inclination B with horizontal plane H = Horizontal component H = B cosδ B = Total field intensity B = √(H² + V²) tan δ = V/H
Fig. 2 — Earth's magnetic elements at an observer's location. α = magnetic declination (angle between geographic and magnetic north). δ = dip/inclination (angle of B with horizontal). H = B cosδ (horizontal component); V = B sinδ (vertical component).
📝 TOPIC-WISE PYQ
Earth's Magnetism — NDA Pattern Questions
Q1. At a place, the angle of dip is 45°. The ratio of horizontal to vertical component of Earth's magnetic field is:
  • (a) 1:1     (b) 1:√2     (c) √2:1     (d) 1:2
Answer: (a) 1:1
tanδ = V/H. At δ = 45°: tan45° = 1 → V/H = 1 → H = V. Ratio H:V = 1:1. Also, H = Bcos45° = B/√2 and V = Bsin45° = B/√2 — confirming equal components.
Q2. At a magnetic pole of the Earth, the angle of dip is:
  • (a) 0°     (b) 45°     (c) 90°     (d) 180°
Answer: (c) 90°
At the magnetic poles, Earth's field is completely vertical (points straight down at N pole, straight up at S pole). The horizontal component H = Bcos90° = 0. Dip = 90°. At the magnetic equator, dip = 0° (field is horizontal).
Q3. Magnetic declination at a place is the angle between:
  • (a) Dip needle and horizontal    (b) Geographic north and magnetic north    (c) Magnetic field and vertical    (d) Earth's axis and magnetic axis
Answer: (b) Geographic north and magnetic north
Magnetic declination is the angle between the geographic meridian (true north-south) and the magnetic meridian (magnetic north-south) at a given location. It tells navigators how much to correct their compass reading from magnetic north to find true north.
Q4. Earth's magnetic field at the equator is:
  • (a) Vertical, pointing down    (b) Horizontal, pointing north    (c) Vertical, pointing up    (d) Zero
Answer: (b) Horizontal, pointing north
At the magnetic equator, dip = 0°. The total field B is entirely horizontal (V = 0, H = B). The direction is from geographic south to geographic north (approximately). This is why a compass needle lies flat and horizontal at the equator.
🤔 TRICKY QUESTIONS
Earth's Magnetism — Navigation Traps
T1. The north-seeking pole of a compass needle points toward Earth's geographic north. Does this mean Earth's geographic north is the magnetic north pole?
No — Earth's geographic north pole corresponds to Earth's magnetic SOUTH pole.
The north-seeking pole (N pole) of a compass is attracted to Earth's geographic north because unlike poles attract. So what exists near geographic north must be Earth's magnetic south pole. Earth's magnetic axis is also tilted ~11.5° from its geographic axis. The "magnetic north pole" that navigators refer to is actually the geographic region near the north, but physically it is Earth's magnetic south pole — this distinction confuses most students.
T2. At a location where the angle of dip is 60°, what is the ratio of the horizontal component to the total magnetic field intensity?
H/B = cos60° = 0.5 (ratio = 1:2)
H = B cosδ = B cos60° = B × 0.5. So H/B = 1/2. Alternatively: V = B sin60° = B√3/2. Check: H² + V² = (B/2)² + (B√3/2)² = B²/4 + 3B²/4 = B² ✓. At 60° dip, horizontal component is only half the total field — the field is steeply inclined at this latitude.

5. Mariner's Compass

5.1
Working Principle & Navigation with a Compass
The instrument that guided explorers — still essential in defence and naval operations

A mariner's compass (magnetic compass) uses a freely pivoted magnetised needle that aligns itself with Earth's magnetic field, with its north-seeking pole pointing toward magnetic north. It is used for direction finding in navigation — at sea, on land, and in aircraft.

⚙ Working Principle

  • Magnetised needle pivoted at its centre on a low-friction bearing
  • Free to rotate in a horizontal plane
  • North pole of needle aligns with Earth's magnetic north
  • Card marked with N, S, E, W and bearings in degrees (0–360°)
  • Compass housed in a liquid-filled bowl (damping — to stop needle oscillating)
  • Gimbals: allow compass to remain horizontal on a rolling ship

📌 Magnetic North vs True North

  • True North (TN): direction toward geographic north pole
  • Magnetic North (MN): direction compass needle points
  • Difference = magnetic declination at that location
  • Navigators apply declination correction to get true bearing
  • True bearing = Magnetic bearing ± Declination
  • Modern GPS: uses magnetic + inertial navigation for accuracy
⚡ Compass Bearings & Declination Correction
True Bearing = Magnetic Bearing + East Declination True Bearing = Magnetic Bearing − West Declination Memory: "East is least, West is best" (for compass to map conversion): East declination: subtract from magnetic bearing → true bearing West declination: add to magnetic bearing → true bearing Example: Compass reads 050° (NE), declination is 5°E True bearing = 050° − 5° = 045° (true northeast) Compass rose: 0°/360° = North; 90° = East; 180° = South; 270° = West Defence applications: Naval navigation: course correction for magnetic declination Artillery: bearing calculations use magnetic + declination data Aircraft: magnetic compass + gyrocompass + GPS combination
N S E W NE SE SW NW N Magnetic North True North α (declination) Mariner's Compass
Fig. 3 — Mariner's compass. Red half of needle = North-seeking pole, aligns with magnetic north. α = declination (angle between magnetic north and true/geographic north). Navigators apply declination correction to find true bearing.
⚓ Defence & Naval Significance: The mariner's compass is among the most important navigation instruments in naval history. Indian Navy vessels use gyrocompasses (independent of Earth's field) combined with magnetic compass backup. Submarine navigation uses magnetic compass calibrated for local declination. Artillery batteries calculate firing directions using magnetic bearings corrected for grid and magnetic declination. A soldier's prismatic compass gives accurate magnetic bearings for reconnaissance.
📝 TOPIC-WISE PYQ
Mariner's Compass & Navigation — NDA Pattern Questions
Q1. A navigator's compass reads a bearing of 080°. The magnetic declination at that location is 10°W. The true bearing is:
  • (a) 090°    (b) 070°    (c) 080°    (d) 060°
Answer: (b) 070°
West declination: True bearing = Magnetic bearing − West declination = 080° − 10° = 070°. (Alternatively: "East is least" → east: subtract from magnetic. "West is best" → west: add to true = 070° + 10° = 080° magnetic ✓)
Q2. Why is the compass needle housed in a liquid-filled bowl?
  • (a) To prevent rusting    (b) To damp oscillations for quicker settling    (c) To increase sensitivity    (d) To make it waterproof
Answer: (b) To damp oscillations for quicker settling
The liquid (usually mineral oil or alcohol) provides viscous damping — when the ship rocks or turns, the needle settles quickly to its equilibrium position instead of oscillating. This gives faster, more readable compass bearings in turbulent conditions.

6. Electromagnets

6.1
Solenoid, Strength & Defence Applications
Current-produced magnetism — controllable, reversible, and enormously powerful

An electromagnet is a magnet made from a coil of wire (solenoid) carrying electric current, usually with a ferromagnetic core. Unlike permanent magnets, its magnetic field can be switched on/off, reversed, and varied in strength — making electromagnets indispensable in modern technology and defence systems.

⚡ Magnetic Field of a Solenoid
Magnetic field inside a solenoid: B = μ₀ n I (infinite solenoid) B = μ₀ μᵣ n I (with ferromagnetic core of relative permeability μᵣ) Where: n = number of turns per unit length (turns/m) I = current through coil (A) μ₀ = 4π × 10⁻⁷ T·m/A μᵣ = relative permeability of core material Factors affecting strength of electromagnet: 1. Number of turns (N) ↑ → strength ↑ 2. Current (I) ↑ → strength ↑ 3. Core material: soft iron (μᵣ ~ 1000s) vs air (μᵣ = 1) 4. Length of solenoid ↓ → field per unit length ↑ (if N fixed) Right-hand thumb rule for solenoid: Curl fingers of right hand in direction of current flow Thumb points toward N pole of solenoid
An air-core solenoid becomes thousands of times stronger with a soft iron core (μᵣ >> 1). Industrial electromagnets can lift hundreds of tonnes of scrap metal — powered by controlling current alone.

🔋 Electromagnet Applications

  • Electric bell and doorbell: electromagnet pulls armature
  • Relay switches: electromagnetic control of circuits
  • Electric motors and generators: rotating magnets
  • Transformers: alternating field in iron core
  • MRI machine: superconducting electromagnets
  • Scrap metal cranes: lifting and releasing metal

🛠 Defence Applications

  • Electromagnetic railgun: Lorentz force accelerates projectile
  • Mine detection: pulsed electromagnetic fields detect metal
  • Submarine detection: SQUID (superconducting) sensors detect field anomalies
  • Degaussing of ships: neutralise ship's magnetic signature to avoid mines
  • Nuclear reactor control rods: electromagnetically positioned
⚠ NDA Key Concept — Degaussing: Naval ships develop a magnetic signature from their steel hull that can trigger magnetic mines. Degaussing is the process of running electric current through coils wound around the ship's hull to neutralise this signature. The term comes from "gauss" (old unit of magnetic field). Degaussing cables are visible on many warships. This is a high-relevance defence application of electromagnetism for NDA candidates.
📝 TOPIC-WISE PYQ
Electromagnets & Applications — NDA Pattern Questions
Q1. The strength of an electromagnet can be increased by:
  • (a) Reducing the number of turns    (b) Increasing current and using a soft iron core    (c) Using a copper core    (d) Reducing current and increasing length
Answer: (b) Increasing current and using a soft iron core
B = μ₀μᵣnI. Strength increases with: more turns (n↑), more current (I↑), and higher permeability core material (μᵣ↑). Soft iron has very high μᵣ (thousands). Copper is non-magnetic (μᵣ ≈ 1) — useless as a core.
Q2. Which technique is used to reduce the magnetic signature of a naval ship and protect it from magnetic mines?
  • (a) Painting with anti-rust paint    (b) Degaussing    (c) Installing echo sounders    (d) Using radar
Answer: (b) Degaussing
Degaussing involves winding electric current-carrying coils around the ship's hull to cancel its magnetic field, making it invisible to magnetic mines. Named after Carl Friedrich Gauss. All modern warships use degaussing systems.
🤔 TRICKY QUESTIONS
Magnetism — Deep Reasoning
T1. A dip needle shows 0° at a location. What can you conclude about that location?
The location is on the magnetic equator.
Dip = 0° means the Earth's total magnetic field B is entirely horizontal — vertical component V = Bsin0° = 0. This only occurs at the magnetic equator, the imaginary circle equidistant from both magnetic poles. Here, H = B (maximum horizontal component). A dip needle lies perfectly horizontal at the magnetic equator.
T2. Can two magnetic field lines ever cross each other? Give a clear explanation.
No — magnetic field lines can never cross.
The tangent to a field line at any point gives the direction of the magnetic field B at that point. If two lines crossed, the field at the crossing point would have two directions simultaneously — which is physically impossible (a field has a unique direction at each point). Therefore, field lines can never intersect. The same rule applies to electric field lines.

⚡ High-Yield Formula Sheet — PN06 Magnetism

📍 Magnetic Dipole
  • M = m × 2l (pole strength × magnetic length)
  • M = I × A (current loop)
  • τ = MB sinθ (torque in field B)
  • U = −MB cosθ (potential energy)
🌎 Earth's Magnetic Elements
  • H = B cosδ (horizontal component)
  • V = B sinδ (vertical component)
  • tan δ = V/H (dip angle)
  • B = √(H² + V²) (total field)
  • δ at poles = 90°; at equator = 0°
🔋 Solenoid / Electromagnet
  • B = μ₀nI (air core)
  • B = μ₀μᵣnI (ferromagnetic core)
  • n = N/L (turns per unit length)
  • Strength ∝ N, I, μᵣ
📋 Magnetic Materials
  • Ferromagnetic: Fe, Co, Ni — strongly attracted
  • Paramagnetic: Al, Pt, O₂ — weakly attracted
  • Diamagnetic: Cu, Bi, H₂O — weakly repelled
  • Steel core: permanent magnet (high retentivity)
  • Soft iron core: electromagnet (low retentivity)
⚓ Compass Navigation
  • True bearing = Magnetic bearing ± Declination
  • East declination: subtract from magnetic bearing
  • West declination: add to magnetic bearing
  • Dip needle: horizontal at equator; vertical at poles
📌 Key Facts
  • Repulsion = sure test of magnetism
  • Breaking magnet → both pieces have N & S poles
  • Field lines: outside N→S; inside S→N (closed loops)
  • Curie temp: Fe 770°C, Ni 358°C, Co 1115°C
  • Geographic N pole ≡ Earth's magnetic S pole
📌 Dimensions: Magnetic moment M = IL² (A·m²); Pole strength m = IL (A·m); Magnetic field B = MT⁻²A⁻¹; Magnetic flux Φ = ML²T⁻²A⁻¹; μ₀ = MLT⁻²A⁻².

⚡ Quick Revision Booster — PN06 Magnetism

📍 Magnet Basics
  • Like poles repel; unlike poles attract
  • Repulsion = only true test of magnetism
  • Breaking magnet → each piece has both poles
  • Monopoles do not exist in nature
  • Poles nearest to ends but NOT exactly at ends
📊 Field Lines
  • Outside: N → S; Inside: S → N (closed loops)
  • Never intersect (unique direction at each point)
  • Denser lines = stronger field (near poles)
  • Tangent at any point = direction of B
🔸 Magnetic Materials
  • Fe, Co, Ni → ferromagnetic (strongly attracted)
  • Al, Pt, O₂ → paramagnetic (weakly attracted)
  • Cu, Bi, water → diamagnetic (weakly repelled)
  • Steel: high retentivity → permanent magnets
  • Soft iron: low retentivity → electromagnets
🌎 Earth's Magnetism
  • Geo. N pole ≡ Earth's magnetic S pole
  • Dip at poles = 90°; at equator = 0°
  • tanδ = V/H; H = Bcosδ; V = Bsinδ
  • At 45° dip: H = V (equal components)
  • Declination: angle between true N and magnetic N
⚓ Compass Navigation
  • Compass points magnetic north, not true north
  • East declination: subtract for true bearing
  • West declination: add for true bearing
  • Liquid damping: stops needle oscillating
  • Gimbals: keep compass horizontal on rolling ship
🔋 Electromagnets
  • B = μ₀μᵣnI (solenoid with core)
  • Strength ↑ with: turns, current, soft iron core
  • Degaussing: cancel ship's magnetic signature
  • Curie temp: heat destroys permanent magnetism
  • RHR: thumb → N pole of solenoid
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