Magnetism and Matter Class 12 Physics Notes | Chapter 5 NCERT Guide
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Class 12 Physics · Chapter 5

Magnetism and Matter: The Complete, No-Confusion Guide

Ever wondered why a compass needle always points north, or why some metals stick to a magnet while others don't? This chapter answers exactly that — and once you see the bar magnet as the hero behind every magnetic phenomenon, from Earth's own magnetic field to the humble refrigerator magnet, it all clicks into place.

📘 NCERT · CBSE · SEBA Aligned ⏱ 30–35 min read ✅ 45+ MCQs Included 🧮 Numericals with Steps

Before We Begin — Why This Chapter Matters

Think about the last time you used a compass app on your phone, or watched an MRI machine in a hospital, or even stuck a shopping list to your fridge with a tiny magnet. All of these — navigation, medical imaging, and that fridge magnet — trace back to the ideas in this one chapter. Magnetism and Matter takes the abstract "magnetic field" from Chapter 4 and grounds it in something you've held in your hands since childhood: the bar magnet.

In this chapter, we zoom out from currents and wires to look at magnets as objects — their field pattern, how the entire Earth behaves like a giant (slightly tilted) bar magnet, and why iron becomes magnetic while wood never does. It's one of the most visual, intuitive chapters in the Class 12 syllabus, and also one of the highest-scoring, because most questions are direct and formula-based.

🎯 Learning Objectives

By the end of this chapter, you will be able to:

  • Describe the magnetic field of a bar magnet and compare it with an electric dipole
  • Derive expressions for the magnetic field on the axial and equatorial lines of a bar magnet
  • Explain why a bar magnet behaves like a solenoid, and derive the equivalence
  • Calculate torque, potential energy, and time period of oscillation of a dipole in a uniform magnetic field
  • State Gauss's law for magnetism and explain why isolated magnetic poles (monopoles) don't exist
  • Define and use the elements of Earth's magnetism: declination, dip (inclination), and horizontal component
  • Explain magnetisation, magnetic intensity, and magnetic susceptibility
  • Classify materials as diamagnetic, paramagnetic, or ferromagnetic using domain theory
  • Distinguish permanent magnets from electromagnets and identify materials suited to each

Chapter Summary — The Big Picture First

Here's the entire chapter in one paragraph, before we go topic by topic. A bar magnet has two poles, North and South, that can never be separated — cut a magnet in half and you just get two smaller magnets, each with its own N and S pole. This "no monopole" rule is the magnetic version of Gauss's law. The magnet's strength is captured by a single number called the magnetic dipole moment (m), and the field it produces looks exactly like the electric field of an electric dipole, just with different constants. Zoom out to planetary scale and Earth itself behaves like a giant bar magnet tilted about 11.3° from its rotation axis — which is why your compass doesn't point to the exact geographic North Pole. Zoom into materials, and every atom is a tiny magnetic dipole due to electron motion and spin; how these tiny dipoles respond to an external field decides whether a material is diamagnetic (weakly repelled), paramagnetic (weakly attracted), or ferromagnetic (strongly attracted, like iron).

🧠 Memory Trick — DPF Rule

Diamagnetic → Pushed away (repelled), weak, no unpaired electrons.
Paramagnetic → Pulled in weakly, has unpaired electrons, aligns temporarily.
Ferromagnetic → Fully committed, strong attraction, forms domains that stay aligned even after the field is removed.

The Bar Magnet & Its Field Lines

Sprinkle iron filings around a bar magnet on a sheet of paper and tap gently — the filings arrange themselves into smooth curved lines running from the North pole, around the outside, back into the South pole, and then continuing inside the magnet from S back to N, forming closed loops. These are magnetic field lines.

N S Field lines exit N, curve around, enter S
Fig 5.1 — Magnetic field lines of a bar magnet, mapped using iron filings or a small compass.

Key Properties of Field Lines

  • They form closed continuous loops (unlike electric field lines, which start and end on charges).
  • Outside the magnet, they go from N to S; inside the magnet, they go from S to N.
  • The tangent to a field line at any point gives the direction of B at that point.
  • Two field lines never intersect (if they did, the field would have two directions at one point, which is impossible).
  • Crowded lines mean a stronger field; widely spaced lines mean a weaker field.
⚠️ Common Misconception

Many students think magnetic field lines "start" at the N pole and "end" at the S pole, the way electric field lines end on a negative charge. In reality, magnetic field lines never end — they continue through the body of the magnet. This is precisely why isolated magnetic monopoles cannot exist.

Magnetic Dipole Moment (m)

A bar magnet is treated as a magnetic dipole — two poles of pole strength qm (also written as just m or p), separated by a vector distance 2l called the magnetic length, directed from S to N.

Magnetic Dipole Moment m = qm × (2l)   (SI unit: A·m², direction S → N)

Magnetic Field on the Axial Line

For a point P on the axis at distance d from the centre of a short bar magnet (d >> l):

Axial Field (short magnet, d ≫ l) Baxial = (μ₀ / 4π) × (2m / d³)

Quick derivation: Treat the magnet as two poles ±qm at distance l from the centre. Field due to N pole at P (distance d−l) is (μ₀/4π)(qm/(d−l)²), directed away from N. Field due to S pole (distance d+l) is (μ₀/4π)(qm/(d+l)²), directed toward S. Both fields point in the same direction along the axis, so they add. Subtracting the two terms, using (d−l)⁻²−(d+l)⁻² ≈ 4dl/d⁴ for d≫l, and substituting m = qm(2l), gives Baxial = (μ₀/4π)(2m/d³).

Magnetic Field on the Equatorial Line

Equatorial Field (short magnet, d ≫ l) Bequatorial = (μ₀ / 4π) × (m / d³)

Notice: Baxial = 2 × Bequatorial for the same distance d. This is exactly analogous to the electric dipole, where the axial field is also twice the equatorial field at the same distance.

📊 The Electrostatic Analogy
Electric DipoleMagnetic Dipole
Dipole moment p = q × 2aDipole moment m = qm × 2l
Eaxial = (1/4πε₀)(2p/r³)Baxial = (μ₀/4π)(2m/r³)
Eequatorial = (1/4πε₀)(p/r³)Bequatorial = (μ₀/4π)(m/r³)
Torque τ = p × ETorque τ = m × B
1/4πε₀ (electric constant)μ₀/4π (magnetic constant)

A Bar Magnet as an Equivalent Solenoid

Ampere's hypothesis: every atom in a magnetic material behaves like a tiny current loop, and a bar magnet is essentially a stack of many such current loops — which is exactly what a solenoid is. This means a current-carrying solenoid should produce the same field pattern as a bar magnet, and it does.

For a solenoid of radius a, total length 2l, with n turns per unit length carrying current I, the field at an axial point at distance d from the centre works out (for d ≫ l, a) to:

Equivalent Solenoid Field B = (μ₀ / 4π) × (2m / d³),   where m = n(2l) × I × πa²

Here, m = NIA (N = total turns, I = current, A = cross-sectional area) — this is the same formula you already know for the magnetic moment of a current loop. This confirms: a bar magnet is equivalent to a solenoid of the same magnetic moment.

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Fig 5.2 — A solenoid's field pattern matches a bar magnet's field pattern exactly.

A Dipole in a Uniform Magnetic Field

Place a bar magnet of moment m in a uniform field B, with the magnet's axis making angle θ with the field. The two poles feel equal and opposite forces (qmB each), which don't cancel in effect — they form a couple that tries to rotate the magnet until it aligns with B.

Torque on a Dipole τ = m × B  →  |τ| = mB sinθ

Work has to be done against this torque to rotate the magnet from angle θ₁ to θ₂, and this work is stored as potential energy:

Potential Energy of a Dipole U(θ) = −m·B = −mB cosθ
  • U is minimum (−mB) when θ = 0° → magnet aligned with field → most stable orientation.
  • U is maximum (+mB) when θ = 180° → magnet anti-aligned → most unstable.
  • U = 0 when θ = 90°, which is conventionally taken as the reference (zero) level of potential energy.

Oscillation of a Dipole — the Vibration Magnetometer Idea

If displaced slightly from θ = 0° and released, the magnet oscillates like a torsion pendulum about the equilibrium position, governed by:

Time Period of Oscillation T = 2π √(I / mB)

where I is the moment of inertia of the magnet about the oscillation axis. This is the working principle of a vibration magnetometer, used to compare magnetic moments or field strengths.

💡 Real-Life Connection

This is exactly why a compass needle settles pointing north-south (θ = 0°, minimum PE) and, if nudged, oscillates back and forth a few times before settling — you can watch this happen with any real compass.

Gauss's Law in Magnetism

Recall Gauss's law in electrostatics: the net electric flux through a closed surface is qenclosed/ε₀. Magnetically, the situation is strikingly different, because isolated magnetic poles (monopoles) do not exist — poles always come in N-S pairs.

Gauss's Law for Magnetism ∮ B · dA = 0  (over any closed surface)

Whatever field lines enter a closed surface, an equal number must leave it, since field lines never terminate. This is the fundamental reason magnetic field lines always form closed loops — it's built into the very structure of magnetism.

🔑 One-Line Definitions to Remember
  • Magnetic declination (D): angle between geographic north and magnetic north at a place.
  • Magnetic dip / inclination (I): angle the Earth's total field makes with the horizontal.
  • Horizontal component (H): the horizontal part of Earth's magnetic field, the part a compass actually responds to.
  • Magnetic susceptibility (χ): ratio of magnetisation to the magnetising field, χ = M/H.
  • Relative permeability (μr): μr = 1 + χ.

Earth's Magnetism — Our Planet, a Giant Bar Magnet

Deep inside Earth, convecting currents of molten iron and nickel in the outer core generate a magnetic field through a self-sustaining "dynamo" process — this is the currently accepted origin (Gilbert first proposed in 1600 that Earth itself is a magnet, though the dynamo mechanism was understood much later). The overall effect is as if a powerful bar magnet were buried near Earth's centre, tilted about 11.3° from the rotation (geographic) axis.

Because of this tilt, the magnet's South pole lies near the geographic North (which is why a compass's North-seeking end points toward geographic north — opposite poles attract), and its geomagnetic poles don't exactly coincide with the geographic poles.

Geographic axis Magnetic axis Sm Nm
Fig 5.3 — Earth's magnetic axis is tilted ~11.3° from its geographic (rotation) axis.

The Three Elements of Earth's Magnetism

At any place, Earth's magnetic field BE is completely described using three quantities, called the magnetic elements:

ElementSymbolMeaning
DeclinationDAngle between geographic meridian and magnetic meridian at a place (how far the compass needle deviates from true north)
Dip / InclinationIAngle between Earth's total field BE and the horizontal plane
Horizontal ComponentHComponent of BE along the horizontal, in the magnetic meridian
Relations Between Elements H = BE cos I    V = BE sin I    tan I = V / H
Horizontal (H) Vertical (V) B_E I
Fig 5.4 — The angle of dip (I) between the total field BE and the horizontal.
🧭 Where Is Dip 0° and Where Is It 90°?

At the magnetic equator, the field is entirely horizontal, so I = 0°. At the magnetic poles, the field is entirely vertical, so I = 90° — this is also why compasses become unreliable near the poles.

Magnetisation and Magnetic Intensity

When a material is placed in a magnetic field, the net magnetic moment per unit volume it develops is called magnetisation (M).

Magnetisation M = mnet / V   (SI unit: A/m)

The magnetic intensity (H) is the external field that causes this magnetisation. The total field inside the material is:

Total Field Inside a Material B = μ₀(H + M)
Magnetic Susceptibility χ = M / H     μr = 1 + χ     μ = μ₀μr

Magnetic Properties of Materials

Every electron orbiting a nucleus is a tiny current loop, and every electron also has an intrinsic "spin" magnetic moment. Whether these tiny atomic magnets cancel out, respond weakly, or lock together strongly decides how a bulk material behaves in a magnetic field.

1. Diamagnetic Materials

In diamagnetic substances, all electrons are paired, so individual atoms have zero net magnetic moment. When placed in an external field, the orbital motion of electrons changes slightly (by Lenz's law) to oppose the applied field — so the induced magnetisation is weak and opposite to B. Diamagnetism exists in all materials, but it's so weak that it's only noticeable when no stronger effect masks it.

Examples: bismuth, copper, water, gold, and — famously — a live frog, which was levitated in a strong magnetic field in a well-known demonstration.

2. Paramagnetic Materials

Here, atoms do have a net magnetic moment (due to unpaired electrons) but these moments point in random directions due to thermal motion, giving zero net magnetisation without a field. On applying an external field, the moments partially align with it, giving weak magnetisation in the same direction as B.

Examples: aluminium, sodium, platinum, oxygen (at low temperature), copper chloride.

3. Ferromagnetic Materials

Ferromagnetic materials have unpaired electron moments that don't just align individually — neighbouring atoms interact so strongly that they form domains: small regions (roughly 1 mm or smaller) where billions of atomic moments are already spontaneously aligned, even without an external field.

Unmagnetised: domains random Magnetised: domains aligned
Fig 5.5 — Domain Theory: an external field aligns the randomly oriented domains, producing strong magnetisation.

When an external field is applied, domains aligned with B grow at the expense of others, producing very strong magnetisation. This alignment can persist even after the field is removed, which is why ferromagnets can become permanent magnets.

Examples: iron, cobalt, nickel, and alloys like alnico.

🌡️ Curie Temperature

Above a certain temperature called the Curie temperature (TC), thermal agitation overcomes the domain alignment, and a ferromagnetic material turns paramagnetic. For iron, TC ≈ 1043 K.

Comparison Table — Dia, Para, and Ferro at a Glance

PropertyDiamagneticParamagneticFerromagnetic
Susceptibility (χ)Small, negative (−1 < χ < 0)Small, positive (0 < χ < ε)Large, positive (χ ≫ 1, up to 10³–10⁵)
Relative permeability μrSlightly less than 1Slightly more than 1Much greater than 1
Behaviour in fieldWeakly repelled, moves to weaker field regionWeakly attracted, moves to stronger field regionStrongly attracted, moves to strongest field region
Effect of temperatureLargely independentχ ∝ 1/T (Curie's Law)χ follows Curie-Weiss law above TC; loses ferromagnetism above TC
Behaves after removing fieldNo memory of fieldNo memory of fieldRetains magnetisation (basis of permanent magnets)
ExamplesBismuth, copper, water, goldAluminium, sodium, platinumIron, cobalt, nickel
Curie's Law (Paramagnetic) χ = C / T     (C = Curie constant, T = absolute temperature)

Permanent Magnets vs Electromagnets

FeaturePermanent MagnetElectromagnet
Material usedSteel, alnico (high retentivity, high coercivity)Soft iron (high permeability, low retentivity)
Hysteresis loopBroad/tall loop — retains magnetism wellThin, tall loop — magnetises and demagnetises easily
Field controlFixed strength, always "on"Strength controlled by current; can be switched off
Everyday useCompass needles, fridge magnets, loudspeakersElectric bells, MRI machines, cranes for lifting scrap iron

Concept Map

                              MAGNETISM AND MATTER
                                      |
        --------------------------------------------------------------
        |                    |                    |                   |
   BAR MAGNET          EARTH'S MAGNETISM      MAGNETIC MATERIALS   GAUSS'S LAW
   - field lines        - declination (D)      - diamagnetic       - no monopoles
   - dipole moment m     - dip (I)              - paramagnetic      - closed flux = 0
   - axial: 2m/4πd³      - horizontal comp (H)  - ferromagnetic
   - equatorial: m/4πd³  - H=Bcos I, V=Bsin I   - domain theory
   - torque τ=mBsinθ                            - Curie temp
   - PE U=-mBcosθ                                - χ, μr, Curie's law
   - as equivalent solenoid
    

Common Misconceptions & How to Avoid Them

❌ Misconception 1

"Field lines start at N and end at S, just like electric field lines end on charges."
✅ Correct: Magnetic field lines are continuous closed loops — they travel N → S outside the magnet and continue S → N inside it. They never truly "end."

❌ Misconception 2

"Cutting a bar magnet in half separates the N and S poles."
✅ Correct: Each half becomes a complete magnet with its own N and S pole — isolated monopoles don't exist.

❌ Misconception 3

"The compass needle points to the geographic North Pole."
✅ Correct: It points toward magnetic north, which differs from geographic (true) north by the angle of declination — and this angle varies from place to place.

❌ Misconception 4

"Diamagnetism only happens in a few special materials."
✅ Correct: Diamagnetism is present in every material (it comes from orbital electron response), but in para- and ferromagnetic materials it's completely overshadowed by the much stronger paramagnetic/ferromagnetic effect.

❌ Misconception 5

"Angle of dip is the same everywhere on Earth."
✅ Correct: Dip varies from 0° at the magnetic equator to 90° at the magnetic poles.

NCERT-Style In-Text & Exercise Questions (Solved)

These are worked in the same style and difficulty as your NCERT exercise questions, with full step-by-step reasoning.

Q1. A short bar magnet has a magnetic moment of 0.9 J/T. Find the magnetic field at a distance of 10 cm from its centre on (a) the axial line and (b) the equatorial line.

Given: m = 0.9 J/T, d = 0.1 m, μ₀/4π = 10⁻⁷ T·m/A

(a) Axial: B = (μ₀/4π)(2m/d³) = 10⁻⁷ × (2×0.9)/(0.1)³ = 10⁻⁷ × 1.8/0.001 = 1.8 × 10⁻⁴ T, directed along the axis.

(b) Equatorial: B = (μ₀/4π)(m/d³) = 10⁻⁷ × 0.9/0.001 = 0.9 × 10⁻⁴ T = half the axial value, as expected.

Q2. A bar magnet of moment 1.5 J/T lies aligned with a uniform field of 0.22 T. What is the work done to turn it (a) by 30° and (b) by 180°?

W(θ) = U(θ) − U(0°) = −mBcosθ − (−mB) = mB(1 − cosθ)

(a) W = 1.5 × 0.22 × (1 − cos30°) = 0.33 × (1 − 0.866) = 0.33 × 0.134 ≈ 0.044 J

(b) W = 1.5 × 0.22 × (1 − cos180°) = 0.33 × 2 = 0.66 J (this is also the maximum possible work since it fully reverses the dipole)

Q3. A short bar magnet placed with its axis at 30° with a uniform external field of 0.16 T experiences a torque of magnitude 0.032 J. Find the magnetic moment of the magnet.

τ = mBsinθ → 0.032 = m × 0.16 × sin30° = m × 0.16 × 0.5 = 0.08m

m = 0.032/0.08 = 0.4 J/T

Q4. A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its N pole pointing down at 22° from the vertical. The horizontal component of Earth's field at that place is 0.35 G. Find the Earth's total magnetic field.

Here the dip from the vertical is 22°, so the dip angle from horizontal is I = 90° − 22° = 68°.

H = BEcos I → BE = H/cos I = 0.35/cos68° = 0.35/0.3746 ≈ 0.934 G

Q5. A sample of paramagnetic salt has 2.0 × 10²⁴ atomic dipoles, each of moment 1.5 × 10⁻²³ J/T. It is placed in a uniform field of 0.64 T, and cooled to 4.2 K. The saturation magnetic moment is 15% of the maximum possible. If the sample is cooled to 2.8 K under a field of 0.98 T, what is the saturation magnetisation now (assume Curie's Law)?

By Curie's Law, magnetisation M ∝ B/T (for a fixed sample). So:

M₂/M₁ = (B₂/T₂)/(B₁/T₁) = (0.98/2.8)/(0.64/4.2) = 0.35/0.1524 ≈ 2.296

M₂ = 2.296 × 15% = ≈ 34.4% of the maximum possible saturation moment

Q6. Explain why a diamagnetic material is repelled by both poles of a strong magnet, while a paramagnetic material is attracted by both poles.

A diamagnetic material develops an induced magnetisation opposite to the applied field (by Lenz's law acting at the atomic level), so it always develops an effective pole of the same kind as the nearby pole of the magnet — hence repulsion, regardless of whether it's the N or S pole nearby. A paramagnetic material's atomic dipoles align along the applied field, developing an opposite pole facing the magnet's pole — hence attraction on either side.

Q7. Why does a magnet dipped in iron filings pick up more filings near its ends than near its middle?

Field lines are most crowded near the poles (ends) of the magnet, so the field — and hence the force on nearby iron filings — is strongest there. Near the middle, the field due to the two poles partially cancels, so fewer filings cling on.

Q8. A solenoid of 400 turns and length 0.20 m, radius 0.01 m, carries a current of 2.5 A. Find its equivalent magnetic moment, and the axial field at 1 m from its centre.

m = NIA = 400 × 2.5 × π(0.01)² = 1000 × π × 10⁻⁴ ≈ 0.314 J/T

B = (μ₀/4π)(2m/d³) = 10⁻⁷ × (2×0.314)/1³ ≈ 6.28 × 10⁻⁸ T

Assertion–Reason, Case Study, HOTS & Board Questions

A. Assertion–Reason Questions

Choose: (a) Both A and R true, R is correct explanation of A (b) Both true, R is not correct explanation (c) A true, R false (d) A false, R true

AR1. Assertion (A): Isolated magnetic monopoles do not exist. Reason (R): Magnetic field lines form closed loops.
Answer: (a) — The absence of monopoles is exactly why field lines have nowhere to terminate and must close on themselves; R correctly explains A.
AR2. Assertion (A): A paramagnetic sample shows greater magnetisation when cooled. Reason (R): Lower temperature reduces the thermal randomisation of atomic dipoles.
Answer: (a) — By Curie's Law χ = C/T, cooling increases susceptibility, and R gives the correct microscopic reason.
AR3. Assertion (A): Soft iron is used for making electromagnets. Reason (R): Soft iron has high retentivity and high coercivity.
Answer: (d) — A is true, but R is false: soft iron has high permeability but low retentivity and low coercivity, which is precisely why it magnetises and demagnetises quickly — ideal for electromagnets.
AR4. Assertion (A): The angle of dip is 90° at the magnetic poles. Reason (R): At the poles, Earth's magnetic field is purely vertical.
Answer: (a) — At the poles H = 0 and the whole field is vertical, so tan I → ∞, i.e., I = 90°.
AR5. Assertion (A): A diamagnetic liquid in a watch-glass placed on top of two magnetic poles collects at the centre. Reason (R): Diamagnetic materials move toward the region of stronger field.
Answer: (c) — A is true (this is a classic demonstration), but R is false: diamagnetic materials move toward the weaker field region, which is why the liquid piles up at the centre (between the poles, away from both pole faces where the field is strongest).

B. Case Study Based Question

📄 Case Study: The Vibration Magnetometer

A student sets up a vibration magnetometer to measure the horizontal component of Earth's field. A small bar magnet of known magnetic moment m and moment of inertia I is suspended so it can oscillate freely in the horizontal plane, under the influence of Earth's horizontal field H. When displaced slightly and released, it executes small oscillations and the student records the time period T.

(i) Write the formula connecting T, I, m, and the horizontal field H.
T = 2π√(I / mH) — same form as T = 2π√(I/mB), with B replaced by the horizontal component H since the magnet oscillates in the horizontal plane.
(ii) If the time period is doubled by using a different magnet of the same mass distribution, how has its magnetic moment changed?
Since T ∝ 1/√m (I and H unchanged), doubling T means m has become one-fourth of its original value.
(iii) Why must this experiment be performed away from other magnets and iron objects?
Any nearby magnet or ferromagnetic object would add its own field to Earth's H, giving a wrong (contaminated) reading for the horizontal component being measured.

C. HOTS & Competency-Based Questions

HOTS1. Two identical bar magnets are placed so that their axes are collinear, N pole of one facing N pole of the other, a small distance apart. Sketch and explain the resultant field pattern at the mid-point between them.
At the exact midpoint, the axial fields due to both magnets point away from each other (both repelling), so by symmetry there's a neutral point along the axis where the net field is zero. Off-axis, the field lines curve outward from this neutral region, resembling the pattern between two like poles.
HOTS2. A ship sailing near the magnetic equator finds its compass reads accurately, but as it sails toward higher latitudes, the compass needle starts to dip and becomes less useful. Explain using the concept of dip.
Near the magnetic equator, dip I ≈ 0°, so Earth's field is almost entirely horizontal and a compass (which responds to H) works well. Moving toward the poles, I increases toward 90°, so H shrinks (H = BEcos I) while the vertical component dominates — the needle tends to dip out of the horizontal plane and the horizontal directive force weakens, making the compass less reliable.
HOTS3 (Competency-based). A furniture company wants a magnetic catch for cabinet doors that stays firmly shut but can be opened by hand. Suggest suitable magnetic material and reasoning.
A ferromagnetic material with moderate retentivity, like a small alnico or ceramic ferrite magnet, is ideal — strong enough to hold the door shut against light forces, but with a field a person can easily overcome by pulling. Soft iron would be unsuitable since it would not retain any magnetism to hold the door.

D. Previous Year Board-Style Questions

PYQ1 (3 marks). Derive an expression for the magnetic field at a point on the equatorial line of a short bar magnet.
Standard derivation: resolve fields due to both poles at the equatorial point, note the components perpendicular to the axis cancel while components along the axis (antiparallel to m) add, and simplify for d≫l to get Beq = (μ₀/4π)(m/d³), directed opposite to m.
PYQ2 (2 marks). Why does a magnetic field line never cross itself?
If two field lines crossed, the field at that intersection point would have two different directions simultaneously, which is physically impossible since the field at any point is a single, uniquely defined vector.
PYQ3 (5 marks). Distinguish between diamagnetic, paramagnetic and ferromagnetic substances on the basis of (a) susceptibility (b) behaviour in a non-uniform field (c) effect of temperature (d) relative permeability.
Refer to the comparison table in the Magnetic Materials section above — this exact structure (four points of comparison) is a favourite 5-mark board question.
PYQ4 (3 marks). Define the term magnetic susceptibility. Write its relation with relative magnetic permeability.
Susceptibility χ = M/H, the ratio of magnetisation to the magnetising field intensity. Relation: μr = 1 + χ, and absolute permeability μ = μ₀(1+χ) = μ₀μr.

Important Numericals — Step by Step

Numerical 1 — Torque & Oscillation

A bar magnet of moment 2.5 J/T and moment of inertia 6 × 10⁻⁶ kg·m² oscillates in a field of 0.04 T. Find its time period.

Step 1: T = 2π√(I/mB)

Step 2: mB = 2.5 × 0.04 = 0.1

Step 3: I/mB = 6×10⁻⁶/0.1 = 6×10⁻⁵

Step 4: √(6×10⁻⁵) ≈ 7.75×10⁻³

Step 5: T = 2π × 7.75×10⁻³ ≈ 0.0487 s ≈ 48.7 ms

Numerical 2 — Finding Dip from Components

At a place, the horizontal component of Earth's field is 0.32 G and the vertical component is 0.44 G. Find the angle of dip and the total field.

Step 1: tan I = V/H = 0.44/0.32 = 1.375

Step 2: I = tan⁻¹(1.375) ≈ 54.03°

Step 3: BE = √(H² + V²) = √(0.1024 + 0.1936) = √0.296 ≈ 0.544 G

Numerical 3 — Susceptibility & Permeability

A paramagnetic material develops a magnetisation of 6 × 10³ A/m in a field of intensity H = 3 × 10⁵ A/m. Find its susceptibility and relative permeability.

Step 1: χ = M/H = 6×10³/3×10⁵ = 0.02

Step 2: μr = 1 + χ = 1.02

Numerical 4 — Comparing Axial and Equatorial Fields

Find the ratio of the axial to equatorial magnetic field of a short bar magnet at the same distance from its centre, and find the distance at which the axial field equals 2 × 10⁻⁵ T for a magnet of moment 0.5 J/T.

Step 1: Ratio Baxial/Beq = 2 (always, at equal distances, for a short dipole)

Step 2: Baxial = (μ₀/4π)(2m/d³) → 2×10⁻⁵ = 10⁻⁷ × (2×0.5)/d³

Step 3: d³ = 10⁻⁷ × 1/(2×10⁻⁵) = 5×10⁻³ → d = (5×10⁻³)^(1/3) ≈ 0.171 m

Numerical 5 — Work Done Against Torque

A magnetic dipole of moment 0.8 J/T is held at 60° to a field of 0.3 T. Find the torque acting on it and the potential energy in this position (taking U = 0 at θ = 90°).

Step 1: τ = mBsinθ = 0.8 × 0.3 × sin60° = 0.24 × 0.866 ≈ 0.208 N·m

Step 2: U = −mBcosθ = −0.8 × 0.3 × cos60° = −0.24 × 0.5 = −0.12 J

Practice MCQ Zone

Tap "Show Answer" after attempting each question yourself — that's how the recall actually sticks.

1. The SI unit of magnetic dipole moment is:

  • A) A/m
  • B) A·m²
  • C) Wb/m
  • D) T·m
Answer: B) A·m² — m = qm × 2l, and since qm effectively carries units linked to current×length, the net SI unit works out to A·m² (same as current × area for a loop).

2. Magnetic field lines of a bar magnet:

  • A) Start at N pole and end at S pole
  • B) Start at S pole and end at N pole
  • C) Form closed continuous loops
  • D) Never exist inside the magnet
Answer: C — they continue inside the magnet from S to N, forming closed loops.

3. The ratio of the axial to equatorial field of a short bar magnet at equal distances is:

  • A) 1
  • B) 2
  • C) 4
  • D) 1/2
Answer: B) 2 — Baxial = 2Bequatorial at the same distance.

4. A bar magnet is equivalent to a solenoid because:

  • A) Both are made of iron
  • B) Both produce an identical external field pattern for the same magnetic moment
  • C) Both have zero magnetic moment
  • D) A solenoid cannot be magnetised
Answer: B

5. The potential energy of a magnetic dipole is minimum when the angle θ between m and B is:

  • A) 0°
  • B) 90°
  • C) 180°
  • D) 45°
Answer: A) 0° — U = −mB, the most negative (minimum) value, meaning maximum stability.

6. Gauss's law for magnetism states that:

  • A) Net flux through any closed surface is q/ε₀
  • B) Net flux through any closed surface is always zero
  • C) Field lines can start inside a closed surface
  • D) Magnetic monopoles exist but are rare
Answer: B

7. The tilt of Earth's magnetic axis from its geographic axis is approximately:

  • A) 0°
  • B) 11.3°
  • C) 23.5°
  • D) 45°
Answer: B) 11.3°

8. Magnetic declination at a place is the angle between:

  • A) Vertical and horizontal component of field
  • B) Magnetic meridian and geographic meridian
  • C) Magnetic field and the ground
  • D) Two magnetic poles
Answer: B

9. The angle of dip at the magnetic equator is:

  • A) 90°
  • B) 45°
  • C) 0°
  • D) 180°
Answer: C) 0° — the field is entirely horizontal there.

10. At the magnetic poles, the horizontal component of Earth's field H is:

  • A) Maximum
  • B) Zero
  • C) Equal to the vertical component
  • D) Negative
Answer: B) Zero — H = BEcos90° = 0.

11. Magnetic susceptibility is defined as:

  • A) M × H
  • B) M / H
  • C) B / H
  • D) H / M
Answer: B) M/H

12. A material with small negative susceptibility is:

  • A) Ferromagnetic
  • B) Paramagnetic
  • C) Diamagnetic
  • D) Non-magnetic
Answer: C) Diamagnetic

13. Which of these is a paramagnetic material?

  • A) Copper
  • B) Bismuth
  • C) Aluminium
  • D) Iron
Answer: C) Aluminium

14. Ferromagnetic materials lose their ferromagnetism above:

  • A) Absolute zero
  • B) Boiling point of water
  • C) Curie temperature
  • D) Room temperature always
Answer: C) Curie temperature

15. Domains in a ferromagnetic material refer to:

  • A) Individual atoms
  • B) Regions with spontaneously aligned atomic moments
  • C) The N and S poles
  • D) Free electrons only
Answer: B

16. Curie's Law for a paramagnetic material states that susceptibility χ is:

  • A) Directly proportional to T
  • B) Inversely proportional to T
  • C) Independent of T
  • D) Proportional to T²
Answer: B) χ = C/T

17. Soft iron is preferred for electromagnet cores because it has:

  • A) High retentivity, high coercivity
  • B) Low retentivity, low coercivity, high permeability
  • C) Zero permeability
  • D) It is non-magnetic
Answer: B

18. Steel is preferred over soft iron for making permanent magnets because steel has:

  • A) Higher retentivity and coercivity
  • B) Lower permeability only
  • C) No hysteresis loop
  • D) Zero magnetic moment
Answer: A

19. The time period of oscillation of a magnetic dipole in a uniform field B is given by:

  • A) T = 2π√(mB/I)
  • B) T = 2π√(I/mB)
  • C) T = 2π(I/mB)
  • D) T = 2π/√(mBI)
Answer: B

20. Relative permeability μr is related to susceptibility χ by:

  • A) μr = χ
  • B) μr = 1 + χ
  • C) μr = 1 − χ
  • D) μr = χ − 1
Answer: B

21. A diamagnetic substance, when placed in a non-uniform field, tends to move toward:

  • A) Stronger field region
  • B) Weaker field region
  • C) Stays where it is
  • D) Along field lines only
Answer: B

22. The magnetic field due to a bar magnet at a point on its equatorial line is directed:

  • A) Parallel to m
  • B) Opposite to m
  • C) Perpendicular to m
  • D) At 45° to m
Answer: B) Opposite to m

23. Torque on a magnetic dipole placed in a uniform field B is given by:

  • A) τ = m·B
  • B) τ = m × B
  • C) τ = m/B
  • D) τ = m + B
Answer: B

24. Which quantity is NOT one of the three elements of Earth's magnetism?

  • A) Declination
  • B) Dip
  • C) Horizontal component
  • D) Magnetic susceptibility
Answer: D

25. A vibration magnetometer works on the principle of:

  • A) Electromagnetic induction
  • B) Oscillation of a dipole in a uniform magnetic field
  • C) Diamagnetism
  • D) Gauss's law
Answer: B

26. Which of the following best explains why a compass fails to work reliably very close to the magnetic poles?

  • A) The field is zero there
  • B) The horizontal component H becomes very small
  • C) Declination becomes negative
  • D) The dip becomes 0°
Answer: B

27. Bismuth is an example of a:

  • A) Ferromagnetic material
  • B) Paramagnetic material
  • C) Diamagnetic material
  • D) Non-metal insulator only, not magnetic at all
Answer: C

28. The magnetic moment of a current loop of area A carrying current I with N turns is:

  • A) NI/A
  • B) NIA
  • C) NI²A
  • D) N/IA
Answer: B) NIA

29. If the angle of dip is 90°, the location is most likely:

  • A) The magnetic equator
  • B) A magnetic pole
  • C) Any random city
  • D) The geographic equator only
Answer: B

30. In the relation B = μ₀(H + M), the term M represents:

  • A) Applied magnetising field
  • B) Magnetisation of the material
  • C) Magnetic moment of a single atom
  • D) Permeability of free space
Answer: B

31. Which statement about paramagnetic materials is correct?

  • A) They retain magnetism after the field is removed
  • B) Their atomic dipoles align randomly without a field and partially align with one
  • C) They have no unpaired electrons
  • D) They are repelled by magnetic fields
Answer: B

32. The hysteresis loop of a material used for permanent magnets should be:

  • A) Thin and tall
  • B) Broad, with high retentivity and coercivity
  • C) A perfect straight line
  • D) Absent entirely
Answer: B

33. Two magnetic field lines of a bar magnet:

  • A) Can intersect at the poles only
  • B) Never intersect each other
  • C) Always intersect at the centre
  • D) Are always straight lines
Answer: B

34. According to Ampere's hypothesis, a bar magnet's magnetism originates from:

  • A) Stationary electric charges
  • B) Atomic-scale current loops
  • C) Gravitational effects
  • D) Nuclear reactions
Answer: B

35. Which of the following pairs is correctly matched?

  • A) Diamagnetic – Iron
  • B) Ferromagnetic – Nickel
  • C) Paramagnetic – Bismuth
  • D) Ferromagnetic – Copper
Answer: B) Ferromagnetic – Nickel

36. If the horizontal component of Earth's field at a place is H and the angle of dip is I, the vertical component V equals:

  • A) H cos I
  • B) H tan I
  • C) H sin I
  • D) H / tan I
Answer: B) V = H tan I (since tan I = V/H)

37. Which best describes the direction of the magnetic dipole moment vector of a bar magnet?

  • A) From N pole to S pole, outside the magnet
  • B) From S pole to N pole, inside the magnet
  • C) Perpendicular to the magnet's length
  • D) Always vertical
Answer: B

38. A neutral point near a bar magnet is a location where:

  • A) The magnet's field is at its maximum
  • B) The magnet's field exactly cancels Earth's field
  • C) Only the vertical component exists
  • D) The compass spins continuously
Answer: B

39. As temperature increases, the susceptibility of a paramagnetic material:

  • A) Increases
  • B) Decreases
  • C) Stays the same
  • D) Becomes negative
Answer: B) Decreases (χ = C/T)

40. Which of these has the highest magnetic susceptibility?

  • A) Diamagnetic material
  • B) Paramagnetic material
  • C) Ferromagnetic material
  • D) Vacuum
Answer: C

41. The unit of magnetic intensity H is:

  • A) A/m
  • B) A·m²
  • C) Tesla
  • D) Weber
Answer: A) A/m

42. A magnet is cut into two equal pieces perpendicular to its length. Each new piece will have:

  • A) Only an N pole
  • B) Only an S pole
  • C) Both N and S poles, with reduced magnetic moment
  • D) No magnetism at all
Answer: C

43. Which effect explains diamagnetism at the atomic level?

  • A) Alignment of unpaired electron spins
  • B) A Lenz's-law-like induced change in electron orbital motion opposing the field
  • C) Formation of magnetic domains
  • D) Nuclear spin resonance
Answer: B

44. For a short bar magnet, if the distance from the centre is doubled, the axial field becomes:

  • A) Half
  • B) One-fourth
  • C) One-eighth
  • D) Double
Answer: C) One-eighth — B ∝ 1/d³, so doubling d gives 1/2³ = 1/8.

45. The Earth's magnetic field is believed to originate from:

  • A) A giant permanent bar magnet buried in the core
  • B) Convective currents of molten metal in the outer core (dynamo effect)
  • C) Solar radiation alone
  • D) Static charge on the crust
Answer: B

Frequently Asked Questions

What is the difference between magnetic dip and declination?
Declination (D) is a horizontal-plane angle — how far magnetic north deviates from true (geographic) north. Dip (I) is a vertical-plane angle — how far Earth's total field tilts down from the horizontal. They describe two completely different directions of deviation.
Why can't we isolate a single magnetic pole?
Every attempt to separate poles — even breaking a magnet down to atomic scale — just creates smaller complete dipoles. This is because magnetism at the atomic level arises from electron current loops and spin, which are inherently dipolar; there's no known "magnetic charge" analogous to electric charge.
Is Earth's magnetic field constant over time?
No — it changes slowly (secular variation) and the magnetic poles drift over years. Over geological timescales, Earth's field has even reversed polarity multiple times, as recorded in rock magnetism.
Why is a diamagnetic effect present in all materials but not always noticeable?
Diamagnetism is a universal but very weak response. In paramagnetic or ferromagnetic materials, the much stronger alignment effects of unpaired electron moments completely overshadow the tiny diamagnetic contribution.
What is the practical difference between using soft iron and steel for magnets?
Soft iron magnetises and demagnetises easily (low retentivity/coercivity) — perfect for electromagnets that need to switch on/off. Steel retains magnetism strongly (high retentivity/coercivity) — ideal for permanent magnets like compass needles.
How is this chapter connected to Chapter 4 (Moving Charges and Magnetism)?
Chapter 4 builds magnetic fields from moving charges and currents (Biot-Savart law, Ampere's law). This chapter treats a bar magnet as an object with its own dipole moment, and shows — via the equivalent solenoid concept — that the two pictures (currents vs. "magnetic poles") are consistent and connected.

One-Page Cheat Sheet

Magnetism and Matter — All Formulas at a Glance

Magnetic moment: m = qm × 2l  |  SI unit: A·m²
Axial field: Baxial = (μ₀/4π)(2m/d³)
Equatorial field: Beq = (μ₀/4π)(m/d³)  |  Baxial = 2Beq
Torque: τ = m × B = mBsinθ
Potential energy: U = −m·B = −mBcosθ
Oscillation period: T = 2π√(I/mB)
Gauss's law (magnetism): ∮B·dA = 0
H = BEcos I  |  V = BEsin I  |  tan I = V/H
Magnetisation: M = mnet/V  |  B = μ₀(H+M)
Susceptibility: χ = M/H  |  μr = 1+χ  |  μ = μ₀μr
Curie's Law: χ = C/T
Diamagnetic χsmall, negative
Paramagnetic χsmall, positive
Ferromagnetic χlarge, positive
Earth's axial tilt≈ 11.3°

Exam Tips, Common Mistakes & Scoring Strategy

✅ Do This
  • Always write the direction along with magnitude for τ, U, and B (vector quantities)
  • Draw a neat labelled diagram for any derivation question — examiners award marks for correct labelling
  • Remember Baxial = 2Bequatorial — a very common one-line question
  • State the "no monopole" reasoning clearly when asked why field lines are closed loops
❌ Avoid This
  • Don't confuse declination (horizontal deviation) with dip (vertical tilt)
  • Don't say soft iron has "high retentivity" — it's the opposite, and this is a favourite trick question
  • Don't forget the negative sign in U = −mBcosθ
  • Don't write χ = H/M — it's the other way round, χ = M/H
🏆 Scoring Strategy

This chapter is short but formula-dense, making it one of the best chapters for guaranteed marks. Master the comparison table (dia/para/ferro) and the Earth's magnetism relations first — together they cover a large share of the 1–3 mark questions almost every year. Then practice the axial/equatorial field derivation and the torque/PE numerical pattern, which reliably shows up as a 3–5 mark question.

Key Takeaways & Conclusion

  • A bar magnet is a magnetic dipole with moment m; its field is mathematically identical in form to an electric dipole's field
  • Magnetic monopoles don't exist — this single fact explains closed field lines, Gauss's law for magnetism, and why cutting a magnet always gives two complete magnets
  • Earth behaves like a giant tilted bar magnet, described completely by declination, dip, and the horizontal component
  • All matter responds to magnetic fields — as diamagnetic, paramagnetic, or ferromagnetic — depending on electron pairing and domain behaviour
  • Permanent magnets need high retentivity (steel); electromagnets need low retentivity, high permeability (soft iron)

Magnetism and Matter is really a story of scale — from a single unpaired electron spin, to a domain, to a bar magnet, all the way up to an entire planet. Once that thread is visible, the formulas stop feeling like things to memorise and start feeling like natural descriptions of something you can literally point a compass at.

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