NCERT Plus Two (Class 12) Physics • Chapter 5

Magnetism and Matter

Bar magnet field lines & solenoid equivalence, dipole torque & energy, Gauss's law in magnetism, M & H relations, and dia/para/ferromagnetic materials.

📄 Official NCERT Textbook PDF

Topic 5.2.1 – 5.2.2: Magnetic Field Lines & Bar Magnet Equivalent Solenoid

Place a bar magnet on your desk next to a copper coil carrying steady battery current, and sprinkle fine iron filings over both. Like magic, the filings trace the exact same swirling loops around both! Even though one looks like a solid metal bar and the other like a spiral spring, deep down a bar magnet behaves just like a tight solenoid packed with tiny atomic current loops!
FIELD LINE RULESForm continuous closed loops (N → S outside, S → N inside); NEVER cross; crowding = stronger B!
NO LONE POLESCut a magnet any way → ALWAYS get 2 smaller N–S magnets! Pole pairs never separate.
SOLENOID EQUIVALENCEFar axial field: B = μ₀4π 2mr³ with m = N I A!
🧠 Memory Trick: Electric field lines are like rivers (start on +, end on −); Magnetic field lines are like roundabouts (always closed loops, N → S outside and S → N inside)!
💡 Simple Kid-Check: Inside a bar magnet, billions of tiny spinning electrons act like microscopic current rings all lined up in one direction. Stack all those tiny rings together and you get the exact magnetic field of a current-carrying solenoid!
  • 1
    Four Field-Line Properties: (i) Always form continuous closed loops without beginning or end. (ii) Tangent at any point gives net magnetic field direction B. (iii) Closer lines mean stronger field (densest near poles). (iv) Two magnetic field lines can NEVER intersect.
  • 2
    Bar Magnet as Equivalent Solenoid: For a finite solenoid of length 2l, radius a, n turns per metre, and current I, the far axial field (r ≫ a, l) is Baxis = μ₀4π 2mr³, matching a bar magnet of magnetic moment m = (2nl) I (πa²) = N I A.
  • 3
    Cutting a Bar Magnet: Magnetic dipole moment m = qm · 2l (unit: A·m² or J/T, pointing S → N). Cut along length (halves area/pole strength qm/2) → new moment m/2. Cut across length (halves length l) → new moment m/2 too!
🧒 Super-Easy Example: A bar magnet of moment M is bent into a semicircular arc of radius R (original length L = πR). Pole separation shrinks from L to diameter 2R = 2L/π, so the new dipole moment becomes M' = qm (2L/π) = 2M / π!
Classic Kerala HSE trap: Students write "magnetic field lines start at North pole and end at South pole." WRONG! That earns zero marks because field lines NEVER stop at poles — they travel North to South outside and continue South to North inside the magnet to form unbroken closed loops!

Topic 5.2.3 – 5.2.4: Dipole Torque, Potential Energy & Electrostatic Analog

Hold a small pocket compass sideways next to a loudspeaker magnet and let go — snap! It whips back straight along the field like a twisted swing! That twisting snap is torque, and the springy energy you pump in while twisting it backward is magnetic potential energy — an exact mirror twin of an electric dipole in Chapter 1!
TORQUE ON DIPOLEτ = m × B ⇒ τ = m B sinθ (Max at 90°, zero at 0°/180°)
POTENTIAL ENERGYU = −m · B = −m B cosθ (Stable: 0°, Unstable: 180°)
WORK TO ROTATEW = U₂ − U₁ = m B (cosθ₁ − cosθ₂) (From 0° → 180°: 2mB!)
🧠 Memory Trick: To switch any Electrostatics dipole formula into Magnetism, just swap p → m, E → B, and 1/ε₀ → μ₀!
💡 Simple Kid-Check: A compass needle loves pointing along B (θ = 0°) where its energy is lowest (−mB, stable like a ball at the bottom of a bowl). Point it directly backwards (θ = 180°) and it sits at the top of a hill (+mB, unstable) — the tiniest nudge flips it right back!
  • 1
    Torque & Time Period: In a uniform field B, forces on N and S cancel (Fnet = 0), leaving pure torque τ = m B sinθ. If displaced slightly from θ = 0°, the needle executes SHM with time period T = 2π √(ImB).
  • 2
    Potential Energy Levels: Choosing U = 0 at θ = 90° gives U(θ) = −m B cosθ. At θ = 0° (parallel, stable), U = −mB; at θ = 180° (antiparallel, unstable), U = +mB.
  • 3
    Exact Dipole Analog Table: Both axial and equatorial fields fall off as 1/r³ at large distances, with Baxial : Beq = 2 : 1 in opposite directions!
PropertyElectrostaticsMagnetism
Constant1 / (4πε₀)μ₀ / (4π)
Dipole Momentp = q · 2am = qm · 2l = N I A
Axial Field (r ≫ l)2p4πε₀ r³μ₀ 2m4π r³
Equatorial Field (r ≫ l)−p4πε₀ r³−μ₀ m4π r³
Torque & Energyp × E , −p · Em × B , −m · B
Watch three classic traps: (1) Rotating a magnet from 0° to 180° requires W = mB(cos 0° − cos 180°) = 2mB, NOT zero! (2) In a uniform magnetic field, net force on a magnet is ALWAYS zero — only torque acts; an iron nail jumps toward a bar magnet because the magnet's field is non-uniform! (3) Notice 1/ε₀ swaps with μ₀ (NOT 1/μ₀!).

Topic 5.3: Gauss's Law for Magnetism (Zero Monopoles)

Imagine holding a transparent plastic bag anywhere in a fast-flowing stream — every litre of water pouring IN through the front of the bag must rush OUT through the back! Now wrap an imaginary Gaussian bag around half a bar magnet, a whole magnet, or empty air: because isolated magnetic "North-only" charges do not exist, every magnetic field line that enters MUST leave!
GAUSS'S LAW (MAGNETISM)ΦB = ∮ B · dA = 0 through ANY closed surface!
CORE MEANINGMagnetic monopoles DO NOT exist! Simplest magnet is a dipole / current loop.
VS ELECTROSTATICSElectric: ∮ E·dA = qenc/ε₀ (can be ≠ 0) • Magnetic: ALWAYS 0!
🧠 Memory Trick: Draw a dotted bag ANYWHERE around a magnet — even chopping across its middle! Lines In (−) ALWAYS equal Lines Out (+), so ΦB(closed) = 0!
💡 Simple Kid-Check: In electricity, you can put a single +q proton inside a box, so lines burst outward and net electric flux isn't zero. In magnetism, there is NO standalone "North particle" (qm)! Even if your box surrounds just the North end of a bar magnet, those same field lines return right inside the metal bar through the box wall!
  • 1
    Mathematical Statement: Divide any closed surface S into tiny patches ΔS. Summing magnetic flux over the entire closed bag gives ΦB = ∑ B · ΔS = ∮ B · dA = 0.
  • 2
    Why It Must Be Zero: Because B lines form unbroken closed loops (N → S outside, S → N inside), any line piercing inward at one spot must pierce outward elsewhere.
  • 3
    What If Monopoles Existed? NCERT points out: if isolated magnetic charges qm existed, Gauss's law for magnetism would read ∮ B · dA = μ₀ qm, just like q/ε₀ in electrostatics!
🧒 Super-Easy Example: Magnetic flux entering five faces of a closed cube totals −0.045 Wb. What must the flux leaving the sixth face be? Since Φtotal = 0, the sixth face MUST carry +0.045 Wb outward!
Watch this subtle exam trap: Gauss's law says flux through a CLOSED 3D surface is zero (∮ B·dA = 0), NOT through a single open flat loop! A single open circular coil clearly has non-zero flux Φ = BA cosθ (which is how generators work in Chapter 6!). Also, zero closed flux does NOT mean B = 0!

Topic 5.4: Magnetisation M, Magnetic Intensity H, Susceptibility & Permeability

Imagine a music teacher setting a steady drum beat inside a school hall (H — the outside effort from a solenoid). Suddenly, all the students start clapping along (M — the material's own atomic response), boosting the total sound in the room (B) up to a thousand times louder!
H AND M DEFINITIONSH = B₀/μ₀ = nI (external effort) • M = mnet/V (material response) • Both in A/m!
MASTER FIELD EQUATIONB = μ₀(H + M) and for linear media M = χ H!
SUSCEPTIBILITY LINKμr = 1 + χ • μ = μ₀ μr = μ₀(1 + χ) • B = μ H!
🧠 Memory Trick: Remember B = μ₀(H + M) like "Total Sound = Speaker (H) + Crowd Clapping (M)"! And μr = 1 + χ always adds the vacuum 1!
💡 Simple Kid-Check: Inside a solenoid core, two actors team up to create total magnetic field B: the free wire current (measured by H) and the material's own aligned atoms (measured by M). Put wood inside → M ≈ 0; put soft iron inside → M explodes to hundreds of times H!
  • 1
    Magnetic Intensity (H): For a long solenoid with n turns/m carrying current I, external magnetising field is H = n I (unit: A m⁻¹). Crucially, H depends ONLY on external currents — NOT on the core material!
  • 2
    Magnetisation (M): Net magnetic dipole moment developed per unit volume of the specimen: M = mnet / V (unit: also A m⁻¹). Material adds extra field Bm = μ₀ M.
  • 3
    Susceptibility (χ) & Permeability (μ): Total field B = B₀ + Bm = μ₀(H + M). For linear materials, M = χ H, giving B = μ₀(1 + χ)H = μ₀ μr H = μ H, where relative permeability μr = 1 + χ (both χ and μr are dimensionless!).
🧒 NCERT Solved Example 5.5: A solenoid of n = 1000 turns/m carries I = 2.0 A with a core of μr = 400.
• H = nI = 1000 × 2 = 2 × 10³ A/m (unchanged by core!).
• B = μr μ₀ H = 400 × (4π × 10⁻⁷) × 2000 ≈ 1.0 T.
• χ = μr − 1 = 399 ⇒ M = χH = 399 × 2000 ≈ 8 × 10⁵ A/m!
Three favorite 1-mark traps: (1) H and M both share the unit A/m, whereas χ and μr are pure dimensionless numbers! (2) Inserting an iron core into a solenoid keeps H = nI constant — only M and B shoot up! (3) Never forget the 1 + in μr = 1 + χ (so if χ = −0.0002, μr = 0.9998, still positive!).

Topic 5.5.1 – 5.5.2: Diamagnetism & Paramagnetism (Curie's Law)

Bring a powerful neodymium magnet near three ordinary items: water actually pushes back slightly like a shy cat (Diamagnetic), aluminium leans in gently (Paramagnetic), while cooling liquid oxygen makes it jump harder toward the poles because cold slows down thermal shaking (Curie's Law)!
DIAMAGNETICWeakly repelled; −1 ≤ χ < 0, 0 ≤ μr < 1; expels field lines; independent of T! (Bi, Cu, H₂O)
PARAMAGNETICWeakly attracted; χ > 0 small, μr > 1; pulls lines in; Curie's Law: χ ∝ 1/T! (Al, Na, O₂)
SUPERCONDUCTORPerfect diamagnet (Meissner effect): B = 0 inside, χ = −1, μr = 0!
🧠 Memory Trick: Dia = "Die-away / Dodge" (repelled, negative χ, ignores temperature); Para = "Pal" (attracted gently, positive small χ, obeys Curie M = C B₀ / T)!
💡 Simple Kid-Check: Every atom has orbiting electrons. When atoms have NO permanent magnetic arrow of their own, an external field tweaks their electron orbits (like tiny Lenz currents) to push back — that's Diamagnetism! When atoms ALREADY carry permanent unpaired magnetic arrows, external field lines them up against heat jiggling — that's Paramagnetism!
  • 1
    Diamagnetism (Universal!): Present in ALL substances (hidden if stronger para/ferro exists). Specimens move from stronger to weaker field regions. Field lines are slightly pushed outside. Examples: Bismuth, Copper, Lead, Silicon, Water, NaCl, Nitrogen.
  • 2
    Superconductors (Meissner Effect): Metals cooled below critical temperature expel magnetic flux completely (B = 0 inside), behaving as perfect diamagnets with χ = −1 and μr = 0 (used in Maglev trains!).
  • 3
    Paramagnetism & Curie's Law: Specimens move slowly from weaker to stronger field regions. Raising temperature shakes dipoles random, so magnetisation follows Curie's Law: M = C B₀T ⇒ χ = C μ₀T ∝ 1T (until saturation at huge B₀/T!).
FeatureDiamagneticParamagnetic
In non-uniform fieldMoves stronger → weaker (repelled)Moves weaker → stronger (attracted)
Susceptibility χSmall negative (~−10⁻⁵)Small positive (~+10⁻⁵ to 10⁻³)
Rel. Permeability μr0 ≤ μr < 11 < μr < 1 + ε
Temperature effectIndependent of Tχ ∝ 1/T (Curie's Law)
Watch three top exam traps: (1) Which magnetic behaviour is universal to all matter? Diamagnetism! (2) Watch negative χ vs temperature: Diamagnetic χ stays constant as temperature rises, whereas Paramagnetic χ drops inversely with Kelvin temperature (χ ∝ 1/T, NOT Celsius!). (3) Superconductor values: χ = −1 and μr = 0!

Topic 5.5.3: Ferromagnetism, Domains, Curie Temperature & Hysteresis Intuition

Why does an iron nail leap across the table to slam onto a fridge magnet while an aluminium spoon barely notices it? Inside iron, trillions of atomic magnets band together into tight cheering squads called domains! When an external magnet says "Attention!", entire squads snap into lockstep at once!
FERROMAGNETIC & DOMAINSStrongly attracted; χ ≫ 1, μr ≫ 1! Macroscopic domains (~1 mm, ~10¹¹ atoms) align spontaneously!
CURIE TEMPERATURE (Tc)Above Tc (Iron: 1043 K), domains melt into a Paramagnet: χ = C/(T − Tc)!
SOFT IRON VS STEELSoft iron: narrow B–H loop, low coercivity (cores/electromagnets). Alnico/Steel: high retentivity + coercivity (permanent magnets).
🧠 Memory Trick: Retentivity = Memory (B left at H=0); Coercivity = Stubbornness (reverse H needed to erase it); Loop Area = Energy wasted as heat per cycle!
💡 Simple Kid-Check: Picture a classroom split into 6 noisy groups facing random directions — overall noise points nowhere (unmagnetised iron!). Now a strict teacher claps once (H): groups facing her grow bigger and rotate straight forward — suddenly a weak push creates an enormous magnetic roar (μr ~ 1000+)!
  • 1
    Domain Alignment (Fe, Co, Ni, Gd): Within each ~1 mm domain (~10¹¹ atoms), atoms align spontaneously. External field B₀ aligns domains by boundary motion & rotation, sucking magnetic field lines tightly inside.
  • 2
    Curie Temperature (Tc): Heat a red-hot iron nail above its Curie temperature (1043 K for Fe, 1394 K for Co, 631 K for Ni) and thermal energy shatters domain order — ferromagnet turns into an ordinary paramagnet!
  • 3
    Hysteresis Loop (B vs H): When magnetising field H returns to zero, B lags behind leaving Retentivity (Br). Reverse field needed to wipe B → 0 is Coercivity (Hc). Area of the closed B–H loop measures heat loss per unit volume per cycle!
ApplicationMaterial ChoiceWhy?
Permanent MagnetSteel, Alnico, TiconalHigh retentivity AND high coercivity (hard to demagnetise)
Electromagnet / Transformer CoreSoft IronHigh permeability, low coercivity, narrow B–H loop (tiny heat loss!)
Top 3-mark DHSE trap: Never write "permanent magnets only need high retentivity"! They MUST have BOTH high retentivity AND high coercivity (so stray fields, vibrations, or temperature bumps can't erase them!). Meanwhile, soft iron beats steel for transformers and electromagnets specifically because its narrow hysteresis loop wastes minimal heat every AC cycle!

Solved Previous Year Questions (Kerala DHSE & NCERT)

Q1 (Kerala HSE March • 2 Marks): State Gauss's law in magnetism. Write two differences between magnetic field lines and electric field lines.

Gauss's Law: The net magnetic flux through any closed surface is zero: ∮ B · dA = 0.
Differences: (1) Magnetic field lines always form closed loops; electrostatic field lines never form closed loops (start at +, end at −). (2) Magnetic monopoles do not exist, whereas isolated electric charges exist.

Q2 (Kerala HSE Say • 2 Marks): A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of 4.5 × 10⁻² J. Find its magnetic moment.

Using τ = m B sinθ:
m = τ / (B sinθ) = (4.5 × 10⁻²) / (0.25 × sin 30°) = (4.5 × 10⁻²) / (0.25 × 0.5) = 0.36 J/T (or A·m²).

Q3 (Kerala HSE Model • 2 Marks): A bar magnet of magnetic moment 0.32 J/T is placed in a uniform field of 0.15 T. Identify its (a) stable and (b) unstable equilibrium orientations and find potential energy in each.

Using U = −m B cosθ (mB = 0.32 × 0.15 = 0.048 J):
• (a) Stable equilibrium: θ = 0° (m ∥ B), Umin = −0.048 J.
• (b) Unstable equilibrium: θ = 180° (antiparallel), Umax = +0.048 J.

Q4 (Kerala HSE March • 2 Marks): Define magnetisation M and magnetic intensity H. Write the relation connecting B, H, and M, and prove μᵣ = 1 + χ.

• Magnetisation (M): Net magnetic moment per unit volume (A/m).
• Magnetic Intensity (H): Magnetising effort H = B₀/μ₀ = nI (A/m).
• B = μ₀(H + M). Substituting M = χH gives B = μ₀(1 + χ)H = μ₀ μᵣ H ⇒ μᵣ = 1 + χ.

Q5 (Kerala HSE Say • 3 Marks): Classify substances into diamagnetic, paramagnetic, and ferromagnetic on the basis of susceptibility χ and behaviour in a non-uniform magnetic field. Give one example of each.

• Diamagnetic: Small negative χ (−1 ≤ χ < 0); weakly repelled toward weaker field (Ex: Bismuth / Water / Copper).
• Paramagnetic: Small positive χ (χ ∝ 1/T); weakly attracted toward stronger field (Ex: Aluminium / Oxygen).
• Ferromagnetic: Very large positive χ (≫ 1); strongly attracted toward stronger field (Ex: Iron / Cobalt / Nickel).

Q6 (NCERT / HSE Model • 1 Marks): What are the values of magnetic susceptibility χ and relative permeability μᵣ for a perfect diamagnet (superconductor)?

Inside a superconductor, B = 0 (Meissner effect). From B = μ₀(1 + χ)H = 0, we get χ = −1 and μᵣ = 0.

Q7 (Kerala HSE March • 2 Marks): State Curie's law in magnetism. What happens to a ferromagnetic substance when heated above its Curie temperature?

Curie's Law: For a paramagnetic material, magnetisation M ∝ B₀/T, so susceptibility χ = C μ₀ / T (inversely proportional to absolute Kelvin temperature T).
Above Curie temperature (Tc), domain order breaks down and a ferromagnet converts into a paramagnet.

Q8 (Kerala HSE March • 3 Marks): Explain the terms retentivity and coercivity. Why is soft iron preferred for electromagnets while steel/Alnico is used for permanent magnets?

• Retentivity: Residual magnetism left in the specimen when external field H is reduced to zero.
• Coercivity: Reverse magnetising field needed to bring residual B back to zero.
• Electromagnets: Soft iron has high permeability, low coercivity, and a narrow hysteresis loop (minimal energy loss).
• Permanent magnets: Alnico/steel has both high retentivity AND high coercivity so magnetism stays locked.