The Magnet Quest — Magnetism and Matter, line by line

STOP 01

Magnetism is everywhere

NCERT 5.1 Introduction · page 136

The book says

"Magnetic phenomena are universal in nature. Vast, distant galaxies, the tiny invisible atoms, humans and beasts all are permeated through and through with a host of magnetic fields from a variety of sources."

In plain words

Magnetism isn't a rare trick that only fridge magnets do. It is everywhere — inside galaxies, inside atoms, inside you. Wherever something with charge is moving, a magnetic field quietly exists.

The book says

"The word magnet is derived from the name of an island in Greece called magnesia where magnetic ore deposits were found, as early as 600 BC."

In plain words

2,600 years ago, people in a Greek place called Magnesia found stones that stuck to iron. They named the stones after their town. That's why we say "magnet" and not something else.

The book says

"In the previous chapter we have learned that moving charges or electric currents produce magnetic fields... credited to Oersted, Ampere, Biot and Savart. In the present chapter, we take a look at magnetism as a subject in its own right."

In plain words

Chapter 4 said: current makes magnetism. Chapter 5 flips it around and asks: what about magnets themselves — bar magnets, the Earth, iron, water? Same physics, new point of view.

The five things the chapter says everyone already knows

1. The Earth behaves as a magnet, with its field pointing roughly from geographic south to geographic north.
2. A freely hanging bar magnet settles north–south. The tip pointing to geographic north is called the north pole; the other is the south pole.
3. North repels north, south repels south, north attracts south.
4. You cannot cut out a lone north pole. Break a magnet and you get two complete magnets. Isolated poles — magnetic monopoles — do not exist.
5. You can make magnets out of iron and its alloys.

The riddle hiding in point 1 and point 2

A magnet's north pole points to the Earth's geographic north. But north attracts south. So what sits near the Earth's geographic north? A magnetic south pole. The Earth is a bar magnet installed upside down. Nobody made a mistake — the naming just came first, and the explanation came 2,000 years later.

Checkpoint · 10 XP

Buried under the Earth's geographic North Pole is which magnetic pole?

STOP 02

The bar magnet has two ends and no middle

NCERT 5.2 The Bar Magnet · Figure 5.1 · page 137

The book says

"We begin our study by examining iron filings sprinkled on a sheet of glass placed over a short bar magnet... The pattern of iron filings suggests that the magnet has two poles similar to the positive and negative charge of an electric dipole."

In plain words

Sprinkle iron dust over a magnet and the dust doesn't scatter randomly — it draws curved lines, thick near the two ends and thin in the middle. Each speck of iron becomes a tiny compass and lines up with the field. The picture is telling you the magnet has two special ends.

Everyday example

Take a fridge magnet and slide a paperclip along it. The clip clings hard at the two ends and almost slips off at the middle. Same message as the iron filings, no lab needed. NCERT uses exactly this trick in Example 5.1(d) to tell a magnet apart from a plain iron bar.

Lab 1 · The compass walk

drag the needle

Drag the little compass anywhere around the magnet. It always turns to point along the field line passing through it. Turn on iron filings to see what the glass sheet in Figure 5.1 actually looks like.

Compass heading: —Field strength here: —

Red end of the needle = its north pole. It swings to point the way B points. Notice the arrows are packed tight near the poles and spread out at the sides — that packing is the strength.

Lab 2 · The unbreakable pair

cut it and see

Point 4 of the introduction says you can never isolate one pole. Try to prove it wrong — cut the magnet as many times as you like.

Cuts made: 0Pieces: 1Lone poles found: 0

Every cut doubles the number of magnets and never once produces a bare N or a bare S. That stubborn fact is what Gauss's law of magnetism will turn into an equation at Stop 07.

Example 5.1 (a) and (b) — worked out

Asked

(a) What happens if a bar magnet is cut (i) across its length, (ii) along its length? (b) Why does a needle in a uniform field feel torque but no force, while an iron nail near a magnet feels a pull too?

Concept

Poles always come in pairs. And: a uniform field pulls both poles equally in opposite directions, so the pulls cancel — only a twist survives.

Solution (a)

Either way you cut it, you get two magnets, each with its own north and south pole. Smaller, weaker, but complete.

Solution (b)

Uniform field ⇒ net force zero, torque m × B not zero. A bar magnet's own field is not uniform — it's stronger near the magnet. The nail gets magnetised (induced moment), and its induced south pole ends up closer to the magnet's north pole than its induced north pole is. Nearer pole feels the stronger pull, so the pulls no longer cancel and the net force is attraction.

Remember

Non-uniform field is the whole reason magnets stick to things. Uniform field can only turn, never tug.

Checkpoint · 10 XP

You cut a bar magnet into 8 equal pieces along its length. How many free north poles now exist?

STOP 03

Four rules that field lines never break

NCERT 5.2.1 The magnetic field lines · Figure 5.2 · page 137–138

The chapter lists four properties. Learn these four and you can spot a wrong diagram instantly — which is exactly what Example 5.3 asks you to do.

Rule (i)

"The magnetic field lines of a magnet (or a solenoid) form continuous closed loops. This is unlike the electric dipole where these field lines begin from a positive charge and end on the negative charge or escape to infinity."

In plain words

A magnetic field line is a racetrack, not a road. It leaves the north pole outside, curls around, dives into the south pole, and then keeps going inside the magnet from S back up to N. No start, no finish. Electric field lines are roads — they begin somewhere and end somewhere.

Rule (ii)

"The tangent to the field line at a given point represents the direction of the net magnetic field B at that point."

In plain words

Wherever you stand on the curve, the direction the curve is heading right there is the direction of B right there. That's why the compass in Lab 1 always lies flat along the line.

Rule (iii)

"The larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B."

In plain words

Crowded lines = strong field. Spread-out lines = weak field. Think of a crowd squeezing through a narrow door — packed means intense.

Rule (iv)

"The magnetic field lines do not intersect, for if they did, the direction of the magnetic field would not be unique at the point of intersection."

In plain words

Two lines crossing would mean a compass at that spot has to point two ways at once. It can't. So lines never cross — not electric ones either.

Footnote worth 4 marks

NCERT deliberately refuses to call these "lines of force." The magnetic force on a moving charge is F = qv × B, which is perpendicular to B — so a charge never travels along a field line. Example 5.4(a) asks this directly and the answer is No.

Lab 3 · Spot the fake diagram

Example 5.3, playable

Each card below is one of the seven diagrams from Figure 5.6. Decide: is it a legal magnetic field picture or not? 6 XP each.

Judged: 0/7Correct: 0

Checkpoint · 10 XP

Inside a bar magnet, which way do the magnetic field lines run?

STOP 04

A bar magnet is a coil in disguise

NCERT 5.2.2 Bar magnet as an equivalent solenoid · Figure 5.3(a) · page 138–139

The book says

"The resemblance of magnetic field lines for a bar magnet and a solenoid suggest that a bar magnet may be thought of as a large number of circulating currents in analogy with a solenoid. Cutting a bar magnet in half is like cutting a solenoid."

In plain words

Ampere's big idea: there is no such thing as "magnet stuff." There are only loops of moving charge. In a coil the loops are wires carrying current. In iron the loops are electrons orbiting and spinning inside atoms. Same physics, different scale.

Why cutting works the same way

Cut a solenoid in half and each half is still a coil — still has a face where current runs anticlockwise (that's the N face) and a face where it runs clockwise (the S face). That's exactly why cutting a magnet never gives you a lone pole. Lab 2 wasn't magic; it was geometry.

The book says

"The magnitude of the field at point P due to the solenoid is B = (μ₀/4π)(2m/r³) ... This is also the far axial magnetic field of a bar magnet."

In plain words

Stand far away on the axis of a coil and far away on the axis of a bar magnet. If you only had a field meter, you could not tell which one you were standing near. The two objects are the same object to the outside world.

B_axial = (μ₀ / 4π) × (2m / r³) valid for r ≫ l

Magnetic moment of a solenoid — the formula that keeps appearing

For a coil of N turns, area A, carrying current I: m = N I A. Exercises 5.3, 5.4 and 5.6 all begin with this one line. Units: A·m² (or equivalently J/T).

Exercise 5.3 — solenoid's magnetic moment

Given

N = 800 turns, A = 2.5 × 10⁻⁴ m², I = 3.0 A

Asked

In what sense does it act like a bar magnet, and what is its magnetic moment?

Concept

A current-carrying solenoid produces the same far field as a bar magnet. Its axis is the N–S line; the end where current looks anticlockwise is the north face.

Formula

m = N I A

Solution

m = 800 × 3.0 × 2.5 × 10⁻⁴ = 800 × 7.5 × 10⁻⁴ = 0.60 J T⁻¹, directed along the solenoid axis.

Exercise 5.6 — moment, force and torque on a suspended solenoid

Given

N = 2000, A = 1.6 × 10⁻⁴ m², I = 4.0 A, B = 7.5 × 10⁻² T, θ = 30°

Formula

m = NIA; F = 0 in a uniform field; τ = mB sin θ

Solution

m = 2000 × 4.0 × 1.6 × 10⁻⁴ = 1.28 J T⁻¹
Force = 0 (the field is uniform — both poles get equal and opposite pulls)
τ = 1.28 × 7.5 × 10⁻² × sin 30° = 1.28 × 0.075 × 0.5 = 4.8 × 10⁻² N·m

Trap

Students write a non-zero force here almost every year. Uniform ⇒ zero net force, always.

Checkpoint · 10 XP

A 500-turn coil of area 4 × 10⁻⁴ m² carries 2 A. Its magnetic moment is

STOP 05

Twisting a magnet, and the energy it stores

NCERT 5.2.3 The dipole in a uniform magnetic field · page 139

The book says

"The torque on the needle is τ = m × B. In magnitude τ = mB sin θ. Here τ is restoring torque and θ is the angle between m and B."

In plain words

Hold a compass sideways to a field and let go. It snaps around. The twist doing that is the torque. It's biggest when the needle sits at 90° to the field, and vanishes when the needle finally lines up.

The book says

"U_m = ∫τ(θ)dθ = ∫mB sin θ dθ = −mB cos θ = −m·B ... potential energy is minimum (= −mB) at θ = 0° (most stable position) and maximum (= +mB) at θ = 180° (most unstable position)."

In plain words

Turning a magnet against the field is like lifting a ball uphill — you have to spend work, and the magnet stores it. Lined up with the field it sits at the bottom of the valley (comfortable, stable). Flipped backwards it balances on the hilltop (one nudge and it flips). Sideways at 90° is exactly halfway, which is why we call that zero energy.

Lab 4 · The torque dial

drag the angle

The grey arrows are a uniform field pointing right. Turn the needle and watch the twist and the stored energy change together.

Angle θ

θ = 55° τ = mB sin θ = — U = −mB cos θ = — State: —

Using m = 1 J T⁻¹ and B = 1 T so the numbers are just sin θ and −cos θ. Watch: torque peaks at 90° where energy is exactly zero. Energy peaks at 180° where torque is back to zero. They are never maximum together.

Everyday example

A door with a spring closer. Push it 90° open and the spring fights hardest (max torque) — but push it all the way to a wobbly balanced position and the spring isn't pulling at that instant, yet it's holding the most stored energy. Magnets do the same thing in a circle.

Exercise 5.1 — find the magnetic moment

Given

θ = 30°, B = 0.25 T, τ = 4.5 × 10⁻² J

Formula

τ = mB sin θ ⟹ m = τ / (B sin θ)

Solution

m = 4.5 × 10⁻² / (0.25 × 0.5) = 4.5 × 10⁻² / 0.125 = 0.36 J T⁻¹

Exercise 5.2 — stable and unstable positions

Given

m = 0.32 J T⁻¹, B = 0.15 T

Concept

U = −mB cos θ. Stable at θ = 0° (m parallel to B), unstable at θ = 180° (antiparallel).

Solution

Stable: m along B, U = −(0.32)(0.15) = −4.8 × 10⁻² J
Unstable: m opposite to B, U = +4.8 × 10⁻² J

Exercise 5.5 — work done to turn a magnet

Given

m = 1.5 J T⁻¹, B = 0.22 T, starts aligned (θ = 0°)

Formula

W = U_final − U_initial = −mB(cos θ₂ − cos θ₁); τ = mB sin θ

Solution (a)

(i) 0° → 90°: W = −mB(0 − 1) = mB = 1.5 × 0.22 = 0.33 J
(ii) 0° → 180°: W = −mB(−1 − 1) = 2mB = 0.66 J

Solution (b)

(i) τ at 90° = mB sin 90° = 0.33 N·m
(ii) τ at 180° = mB sin 180° = 0

Notice

At 180° the magnet has maximum energy but feels zero twist. Perfectly balanced — and perfectly ready to fall.

Checkpoint · 12 XP

At which angle is the torque on a magnetic dipole maximum and its potential energy zero?

STOP 06

Steal the answers from electrostatics

NCERT 5.2.4 The electrostatic analog · Table 5.1 · page 140–141

The book says

"...magnetic field at large distances due to a bar magnet of magnetic moment m can be obtained from the equation for electric field due to an electric dipole of dipole moment p, by making the following replacements: E → B, p → m, 1/4πε₀ → μ₀/4π."

In plain words

You already solved all of this in Chapter 1 — for electric dipoles. So don't learn new formulas. Learn a swap rule: replace E with B, p with m, and 1/4πε₀ with μ₀/4π. Every electric dipole formula instantly becomes a magnetic one.

Quantity	Electrostatics	Magnetism
Constant	1/ε₀	μ₀
Dipole moment	p	m
Equatorial field (short dipole)	−p / 4πε₀r³	−μ₀m / 4πr³
Axial field (short dipole)	2p / 4πε₀r³	μ₀ 2m / 4πr³
Torque in external field	p × E	m × B
Energy in external field	−p·E	−m·B

The one line that catches people

The axial field is twice the equatorial field at the same distance, and the two point in opposite directions. On the axis, B points the same way as m. On the equator, B points opposite to m — that's what the minus sign in equation 5.4 is doing.

Lab 5 · Axial vs equatorial

slide the distance

Move the probe and compare the field at the same distance on the axis and on the equator of the same short magnet.

Distance r

r = — cm B_axial = — B_equat = — Ratio = 2.00

Computed with m = 0.48 J T⁻¹, exactly the magnet from Exercise 5.7. Halve the distance and the field grows eight-fold — because of that r³.

Exercise 5.7 — axial and equatorial field of a short magnet

Given

m = 0.48 J T⁻¹, r = 10 cm = 0.10 m, μ₀/4π = 10⁻⁷ T·m·A⁻¹

Formula

B_axial = (μ₀/4π)(2m/r³); B_equatorial = (μ₀/4π)(m/r³)

Solution (a)

B = 10⁻⁷ × (2 × 0.48) / (10⁻³) = 10⁻⁷ × 960 = 0.96 × 10⁻⁴ T, directed along the axis from S to N — i.e. along m.

Solution (b)

B = 10⁻⁷ × 0.48 / 10⁻³ = 0.48 × 10⁻⁴ T, directed opposite to m (from N to S).

Example 5.2 — stable, unstable and lowest-energy arrangements

Concept

Needle Q sits in the field made by needle P. Energy U = −m_Q·B_P. So: stable when m_Q is parallel to B_P, unstable when antiparallel, no equilibrium when perpendicular.

Answer (a)

Not in equilibrium: PQ₁ and PQ₂ (m_Q is perpendicular to B_P there, so a torque remains).

Answer (b)

Stable: PQ₃ and PQ₆. Unstable: PQ₅ and PQ₄.

Answer (c)

Lowest potential energy: PQ₆ — it sits on the axis, where B_P is twice as strong, and it is aligned with it.

Why PQ₆ beats PQ₃

Both are stable, but the axial field is 2× the equatorial field. Same alignment, stronger field ⇒ deeper energy well.

Checkpoint · 12 XP

At the same distance r from a short bar magnet, B_axial ÷ B_equatorial equals

STOP 07

Gauss's law: nothing ever leaks out

NCERT 5.3 Magnetism and Gauss's Law · Figure 5.5 · page 142–143

The book says

"...the number of magnetic field lines leaving the surface is balanced by the number of lines entering it. The net magnetic flux is zero for both the surfaces. This is true for any closed surface."

In plain words

Draw any imaginary closed bag anywhere — around a pole, around the whole magnet, in empty space, any shape at all. Count the field lines going in and the field lines coming out. They always match exactly. Nothing is created inside, nothing is destroyed inside.

φ_B = Σ B · ΔS = 0 (compare: Σ E · ΔS = q / ε₀)

The book says

"The difference between the Gauss's law of magnetism and that for electrostatics is a reflection of the fact that isolated magnetic poles (also called monopoles) are not known to exist. There are no sources or sinks of B."

In plain words

Electricity has a zero on the wrong side: q/ε₀. You can trap a lone positive charge in a bag, so electric flux can be non-zero. Magnetism's right-hand side is a flat 0 because you can never trap a lone north pole. Lab 2 proved it with scissors; this is the same fact written in maths.

Lab 6 · The flux auditor

count them yourself

Pick a surface and run the audit. Guess the net flux before you press the button — it never changes.

Lines entering: — Lines leaving: — Net flux φ_B: —

Example 5.4 — four short conceptual questions

(a)

Do field lines show the force on a moving charge? No. The magnetic force is qv × B, always perpendicular to B, so calling them "lines of force" is misleading.

(b)

If monopoles existed, Gauss's law becomes ∮B·ds = μ₀q_m, where q_m is the magnetic charge enclosed — exactly mirroring the electric version.

(c)

Does a magnet twist itself? No. No element feels a force from the field it makes itself. But a different element of the same wire can push on it (and for a straight wire that force is zero).

(d)

Can something with zero net charge have a magnetic moment? Yes. An atom is electrically neutral, yet its circulating electrons make current loops with real magnetic moments. That's the entire basis of paramagnetism.

Checkpoint · 12 XP

A closed surface encloses only the north pole of a bar magnet. The net magnetic flux through it is

STOP 08

Splitting the field into "mine" and "yours"

NCERT 5.4 Magnetisation and Magnetic Intensity · page 145–146

The book says

"We define magnetisation M of a sample to be equal to its net magnetic moment per unit volume: M = m_net/V."

In plain words

Every atom is a microscopic magnet. Add up all their moments and divide by how much space they take up. That's M — how magnetised the material has become, packed per cubic metre. Units: A m⁻¹.

The book says

"B = B₀ + B_m ... B_m = μ₀M ... H = B/μ₀ − M, so B = μ₀(H + M)."

In plain words

Inside a filled solenoid the field has two owners.
H is your contribution — it depends only on the current you pushed through the coil (H = nI). Turn the knob and H changes; the material has no say.
M is the material's contribution — how much the iron woke up and joined in.
Add both and you get the real field B.

Everyday example

You shout into a canyon. H is your own voice. M is the echo the canyon adds. B is everything a listener actually hears. A soft canyon (diamagnetic) gives a slightly negative echo and you hear a bit less. A stone canyon (ferromagnetic) gives an echo a thousand times louder than your shout.

The book says

"M = χH ... χ is small and positive for materials which are called paramagnetic. It is small and negative for materials which are termed diamagnetic."

In plain words

χ (chi, "kai") is the eagerness number: how keenly a material joins in when you apply a field. Positive means it helps. Negative means it pushes back. Big means it goes wild.

M = χH · B = μ₀(1 + χ)H = μ₀μ_rH = μH · μ_r = 1 + χ

Only one of them is really independent

χ, μ_r and μ are three faces of the same number. Give me any one and I'll hand you the other two: μ_r = 1 + χ, and μ = μ₀μ_r. χ and μ_r carry no units at all; μ carries the same units as μ₀.

Example 5.5 — the four-part solenoid calculation

Given

μ_r = 400, I = 2.0 A, n = 1000 turns per metre

Asked

Find H, M, B and the magnetising current I_M.

(a) H

H depends only on the coil, never on the core: H = nI = 1000 × 2.0 = 2 × 10³ A/m

(b) B

B = μ_rμ₀H = 400 × 4π × 10⁻⁷ × 2 × 10³ ≈ 1.0 T

(c) M

M = (B − μ₀H)/μ₀ = (μ_r − 1)H = 399 × 2 × 10³ ≈ 8 × 10⁵ A/m

(d) I_M

The extra current you'd need in a bare coil to fake the core's help. From B = μ₀n(I + I_M) with B = 1 T, I = 2 A: I_M ≈ 794 A

Feel it

You supplied 2 amperes. The iron behaved as though someone quietly added 794 more. That is what "the material joins in" really means.

Checkpoint · 12 XP

You slide an iron core into a current-carrying solenoid without changing the current. What happens to H inside?

STOP 09

Three kinds of material, three personalities

NCERT 5.5 Magnetic Properties of Materials · Table 5.2 · Figures 5.7, 5.8 · page 147–149

Property	Diamagnetic	Paramagnetic	Ferromagnetic
Susceptibility χ	−1 ≤ χ < 0	0 < χ < ε (small)	χ ≫ 1
Relative permeability μ_r	0 ≤ μ_r < 1	1 < μ_r < 1 + ε	μ_r ≫ 1 (>1000)
Permeability μ	μ < μ₀	μ > μ₀	μ ≫ μ₀
Field lines inside	Pushed out, field reduced	Pulled in slightly, field raised	Crowded in heavily
In a non-uniform field	Moves strong → weak	Moves weak → strong	Moves weak → strong, strongly
Examples	Bismuth, copper, lead, silicon, nitrogen (STP), water, NaCl	Aluminium, sodium, calcium, oxygen (STP), copper chloride	Iron, cobalt, nickel, gadolinium, alnico

Diamagnetism · the book says

"Diamagnetic substances are the ones in which resultant magnetic moment in an atom is zero. When magnetic field is applied, those electrons having orbital magnetic moment in the same direction slow down and those in the opposite direction speed up... the substance develops a net magnetic moment in direction opposite to that of the applied field and hence repulsion."

In plain words

These atoms started with zero magnetism — everything cancelled. Then a field arrives and nudges the orbiting electrons: some slow, some speed up. The leftover is a tiny magnet pointing backwards. That's why the sample gets gently pushed away. (Lenz's law, which you meet in Chapter 6, is the reason it's backwards and not forwards.)

The superstar: superconductors

Cool certain metals far enough and they become perfect diamagnets: χ = −1 and μ_r = 0. The field lines are completely thrown out — not reduced, expelled. This is the Meissner effect. It's how magnetically levitated trains float, and why a magnet hovers over a chilled superconductor puck.

NCERT adds: diamagnetism exists in everything, but it's so weak (about one part in 10⁵) that para- or ferromagnetism drowns it out whenever they're present.

Paramagnetism · the book says

"The individual atoms... possess a permanent magnetic dipole moment of their own. On account of the ceaseless random thermal motion of the atoms, no net magnetisation is seen. In the presence of an external field B₀, which is strong enough, and at low temperatures, the individual atomic dipole moment can be made to align."

In plain words

Every atom here is already a little magnet — but heat keeps jostling them into random directions, so they cancel out. Apply a field and they start to line up. Cool the sample down and they line up better, because there's less jiggling to fight. Enough field or enough cold and they all point the same way: saturation.

Ferromagnetism · the book says

"...they interact with one another in such a way that they spontaneously align themselves in a common direction over a macroscopic volume called domain... Typical domain size is 1 mm and the domain contains about 10¹¹ atoms."

In plain words

Here the atoms don't wait for you. They form gangs — domains — of about a hundred billion atoms each, all already pointing the same way. Fresh iron looks unmagnetised only because the gangs point in random directions and cancel. Apply a field and two things happen at once: the gangs turn to face the field, and the gangs that already faced it grow bigger by eating their neighbours.

Lab 7 · Command the domains

field vs heat

Each arrow is a domain. Raise the field to align them. Then raise the temperature and watch your army fall apart.

Field B₀

Temperature

Alignment: — Bulk magnetisation M: — Behaving as: —

Push the temperature to the top with the field on and the domain structure disintegrates — a ferromagnet turns into a paramagnet. NCERT: "At high enough temperature, a ferromagnet becomes a paramagnet."

Hard vs soft — the difference that builds devices

Hard ferromagnets keep their magnetisation after you switch the field off. Alnico (iron + aluminium + nickel + cobalt + copper) and natural lodestone are hard. These become permanent magnets — compass needles, speaker magnets.

Soft ferromagnets lose it the moment the field goes. Soft iron is the classic. These become electromagnet cores and transformer cores, where you need the magnetism to switch off on command.

Lab 8 · Sort the materials

boss-level sorting

Tap a material, then tap the bin it belongs in. 5 XP for each correct drop. All twelve come straight from the chapter.

Diamagnetic

χ negative · pushed away

Paramagnetic

χ small positive · weakly pulled

Ferromagnetic

χ huge · strongly pulled

Sorted: 0/12Correct: 0

Checkpoint · 12 XP

A rod hangs freely between two magnetic poles and turns to sit at right angles to the field, moving toward the weaker region. The rod is

STOP 10

The treasure chest

NCERT Summary + Points to Ponder · page 149–152

Everything the chapter asks you to carry out of it, on one page.

τ = m × B, |τ| = mB sin θ U = −m · B = −mB cos θ (zero fixed at θ = 90°) W = −mB(cos θ₂ − cos θ₁) B_axial = μ₀m / 2πr³ · B_equatorial = −μ₀m / 4πr³ m_solenoid = N I A φ_B = Σ B · ΔS = 0 (Gauss's law for magnetism) H = B₀ / μ₀ = nI · M = m_net / V · B = μ₀(H + M) M = χH · μ_r = 1 + χ · μ = μ₀μ_r · B = μH

Points to Ponder, in one breath each

1. People used compasses for 2,000 years before anyone understood why they worked. Engineering does not wait for theory.
2. Charge is quantised and lone charges exist; magnetic poles are neither. We still don't know why.
3. No monopoles ⇒ field lines must close on themselves. Electric lines are allowed to start and stop.
4. χ ≈ −10⁻⁵ vs χ ≈ +10⁻⁵ — a difference in the fifth decimal place flips the entire behaviour from repelled to attracted.
5. A superconductor is a perfect diamagnet and a perfect conductor. No classical theory joins those two facts; BCS theory (1957) did, and won the 1972 Nobel Prize.
6. Diamagnetism is universal — present in everything, just usually invisible.
7. Dia, para and ferro aren't the whole list. Ferrimagnetic, anti-ferromagnetic and spin glass materials exist too.

Five traps this chapter sets

1. "Uniform field ⇒ some force." No. Uniform field gives torque only; force is exactly zero.
2. Forgetting the axial field is 2× the equatorial, and points the opposite way.
3. Thinking H changes when you insert a core. H = nI. It doesn't.
4. Writing μ_r = χ instead of μ_r = 1 + χ.
5. Saying magnetic field lines are lines of force. They are not — force is perpendicular to them.

Boss quiz

Six questions, 15 XP each. Clear five of them and the last badge unlocks.

Boss 1 · 15 XP

A magnetic needle of moment 2 J T⁻¹ sits at 60° to a 0.5 T uniform field. The torque on it is

Boss 2 · 15 XP

A material has χ = −0.00001. Its relative permeability μ_r is

Boss 3 · 15 XP

Work done to rotate a dipole from the stable position all the way to the unstable position is

Boss 4 · 15 XP

Which statement about a toroid is correct, following Example 5.1(c)?

Boss 5 · 15 XP

Heat a ferromagnetic material above a high enough temperature and it becomes

Boss 6 · 15 XP

For a superconductor exhibiting the Meissner effect, the pair (χ, μ_r) is

Badge shelf

Seven to collect.

Final standing

Magnet Master?

Iron Filing 0 XP · 0/7 badges

You've walked the whole of Chapter 5: poles, field lines, the solenoid disguise, torque and energy, the electrostatic swap rule, Gauss's law, H and M and χ, and the three personalities of matter. Come back and beat your own XP — the quiz answers reset every time you reload.