Magnetism and Matter

2.1 Core concepts

Magnetism is older than the science of it. The word "magnet" comes from Magnesia, a region in Greece where lodestone (a naturally magnetic form of magnetite) was found around 600 BC. Magnetic compasses guided ships across the medieval world long before the laws of electromagnetism were written down. The Earth itself behaves like a giant bar magnet whose field points approximately from geographic south to geographic north, which is what a compass needle responds to (NCERT §5.1, p. 136).

Some basic facts emerge from simple experiments with a bar magnet (NCERT §5.1, p. 137). A freely suspended bar magnet aligns itself along the geographic north–south direction; the end pointing to geographic north is the north pole (N), the other the south pole (S). Like poles repel, unlike poles attract — a Coulomb-like rule. Sprinkling iron filings around a bar magnet traces a family of curves running from N to S externally and from S to N internally, identical in shape to the lines of force of a current-carrying solenoid. Most importantly, magnetic monopoles do not exist: cutting a bar magnet across its length produces two smaller bar magnets, each with its own N and S, no matter how many times you cut. The simplest magnetic element is therefore a dipole, not a charge.

The deep theoretical statement underlying this is Ampere's hypothesis: every magnetic effect is ultimately due to circulating electric currents. A bar magnet is equivalent to a stack of microscopic current loops, each loop carrying a tiny circulating current (NCERT §5.2.2, p. 138). Hence a bar magnet of magnetic moment m and a long solenoid carrying an appropriate current produce the same field pattern far away. The far axial field of a finite solenoid worked out from the Biot–Savart law is B_A = (μ₀/4π) × (2m/r³), identical to that of a bar magnet of dipole moment m (NCERT §5.2.2, Eq. 5.1, p. 139).

Properties of magnetic field lines (NCERT §5.2.1, p. 137–138). (i) Magnetic field lines form continuous closed loops, unlike electric field lines which start on positive charges and end on negative charges. (ii) The tangent to a field line at any point gives the direction of B there. (iii) The density of field lines per unit area perpendicular to them is proportional to |B|, so closely spaced lines indicate strong field. (iv) Field lines never intersect — if they did, B would have two directions at the same point.

Torque and energy of a dipole in a uniform field (NCERT §5.2.3, p. 139). Consider a bar magnet placed in a uniform external field B at angle θ to it. The forces on the N and S poles are equal and opposite, so the net force is zero; but they form a couple producing a torque

τ = m × B, with magnitude τ = mB sin θ (Eq. 5.2, p. 139).

Doing work against this restoring torque to rotate the dipole stores potential energy

U = −m·B = −mB cos θ (Eq. 5.3, p. 139).

The zero of energy is chosen at θ = 90°. The minimum U = −mB is at θ = 0° (m parallel to B — most stable orientation); the maximum U = +mB is at θ = 180° (m anti-parallel — most unstable). These results, with τ → 0 at both extremes, look exactly like an electric dipole in an electric field. The general electrostatic-magnetic analogy is summarised in NCERT Table 5.1, p. 141: replacing E → B, p → m and 1/(4πε₀) → μ₀/4π converts every electrostatic dipole formula into its magnetic counterpart. For a short bar magnet on the axis at distance r from the centre, B_A = (μ₀/4π)(2m/r³), and on the equatorial plane B_E = −(μ₀/4π)(m/r³) (NCERT §5.2.4, Eqs. 5.4–5.5, p. 140). The equatorial field is anti-parallel to m and half the axial field's magnitude — a frequent CUET trap.

Gauss's law for magnetism (NCERT §5.3, p. 142–143). Because magnetic field lines form closed loops, every line entering a closed surface must also exit it. Hence the net magnetic flux through any closed surface is zero:

φ_B = ∮ B · dS = 0 (Eq. 5.6, p. 143).

This is the magnetic analog of Gauss's law for electricity, but with the right-hand side zero — a direct statement that no magnetic monopoles exist (no sources or sinks of B). In Maxwell's equations this becomes ∇·B = 0.

Magnetisation, intensity and permeability (NCERT §5.4, p. 145–146). Inside a magnetic material, the dipoles of individual atoms produce a net magnetic moment per unit volume:

M = m_net / V (Eq. 5.7, p. 145), units A m⁻¹.

Inside a solenoid of n turns per metre carrying current I, the field would be B₀ = μ₀ nI in vacuum. When the bore is filled with a magnetic material, the material contributes an additional field B_m = μ₀ M, so the total field is B = B₀ + B_m = μ₀(nI + M). To separate the contribution of free conduction currents from that of the material, one defines the magnetic intensity (or magnetising field)

H = B/μ₀ − M (Eq. 5.10, p. 146), units A m⁻¹.

Equivalently B = μ₀(H + M). For linear, isotropic materials the magnetisation is proportional to H:

M = χH (Eq. 5.13, p. 146),

where χ is the dimensionless magnetic susceptibility. Substituting back gives B = μ₀(1 + χ)H = μ₀ μr H = μH, where μr = 1 + χ is the relative permeability (dimensionless) and μ = μ₀μr is the magnetic permeability of the material.

Classification of magnetic materials (NCERT §5.5, p. 147, Table 5.2). All materials fall into three broad classes:

• Diamagnetic (−1 ≤ χ < 0, 0 ≤ μr < 1, μ < μ₀). Atoms have zero net moment; on applying B, induced currents (a manifestation of Lenz's law) produce a moment that opposes B. The substance is feebly repelled by a magnet, moves from regions of strong to weak field, and the field lines tend to be expelled from its interior (NCERT §5.5.1, p. 147–148, Fig. 5.7a). Examples: bismuth, copper, lead, silicon, nitrogen at STP, water, sodium chloride. Superconductors are perfect diamagnets with χ = −1, μr = 0; they completely expel the magnetic field, a phenomenon known as the Meissner effect.
• Paramagnetic (0 < χ < ε, 1 < μr < 1 + ε, μ slightly > μ₀). Each atom carries a permanent magnetic moment, but thermal motion randomises them, so the bulk substance has no net M in zero field. An external B partially aligns the moments along itself; the field lines crowd into the material (Fig. 5.7b), the substance is feebly attracted by a magnet and moves from weak to strong field regions. Susceptibility and μr depend on temperature (Curie's law). Examples: aluminium, sodium, calcium, oxygen at STP, copper chloride (NCERT §5.5.2, p. 148).
• Ferromagnetic (χ ≫ 1, μr ≫ 1). Quantum mechanical exchange interaction causes atomic moments to align spontaneously over macroscopic regions called domains (~1 mm size, ~10¹¹ atoms each). In an unmagnetised piece the domains are randomly oriented and cancel out; an applied B grows favourably-oriented domains at the expense of others, until they merge into one giant domain at saturation (NCERT Fig. 5.8, p. 149). The resulting M can be enormous, μr > 1000. Hard ferromagnets (Alnico, lodestone) retain their magnetisation when the external field is removed — these are used as permanent magnets. Soft ferromagnets (soft iron) lose their magnetisation almost completely — used in transformer and motor cores. Above a critical (Curie) temperature, thermal motion destroys the domain order and a ferromagnet becomes paramagnetic. Examples: iron, cobalt, nickel, gadolinium. Diamagnetism is universal — every substance has a small diamagnetic contribution from induced currents — but in paramagnetic or ferromagnetic materials the much stronger paramagnetic/ferromagnetic response masks it.

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 5.1 (p. 137): Iron filings around a bar magnet — shows the dipole field pattern, concentrated near the poles.
• Fig. 5.2 (p. 138): Field lines of (a) bar magnet, (b) finite current-carrying solenoid (identical pattern), (c) electric dipole, with hypothetical Gaussian surfaces marked.
• Fig. 5.3 (p. 138): Axial field calculation for a finite solenoid (analogy with bar magnet); compass needle in uniform B.
• Fig. 5.5 (p. 142): A vector area element ΔS of a closed surface S used to define magnetic flux φ_B = Σ B·ΔS, which is zero for any closed surface.
• Fig. 5.7 (p. 147): Behaviour of field lines near (a) a diamagnetic specimen — lines are expelled, less dense inside; (b) a paramagnetic specimen — lines concentrate inside, more dense.
• Fig. 5.8 (p. 149): Domains in a ferromagnet — (a) randomly oriented (no bulk M); (b) aligned in external B (single giant domain).
• Table 5.1 (p. 141): Electrostatics ↔ Magnetism dipole analogy table — the key cheat-sheet for converting electric-dipole results to magnetic ones.
• Table 5.2 (p. 147): χ, μr, μ ranges for dia-, para- and ferromagnetic materials.

2.4 Common confusions / NTA trap points

• Magnetic field lines are NOT lines of force on a moving charge — the magnetic force qv × B is perpendicular to B, not along the field lines (NCERT Example 5.4(a), p. 144).
• B_E and B_A differ by a factor of 2: B_A = 2 × |B_E| for a short bar magnet on the same r. Watch the sign of B_E (anti-parallel to m on the equatorial line).
• Diamagnetism is present in all substances but is masked in para-/ferromagnets — students often pick "only some substances" as a distractor (NCERT Points to Ponder 6, p. 151).
• For diamagnetic materials, χ is negative (so M and H are anti-parallel) and μr < 1 — easy to confuse with paramagnetic.
• "Bar magnet exerts torque on itself" — NO. An element of a body does not exert a force/torque on itself due to its own field (Example 5.4(c), p. 145).
• Magnetic flux through a closed surface is always zero — even if it appears to enclose a "north pole" — because monopoles don't exist (NCERT §5.3, p. 143).
• Forgetting μr = 1 + χ (not 1 − χ or χ − 1) — the +χ sign is a frequent NTA distractor.
• Confusing "soft" with "soft material" — in magnetism "soft" means easy to demagnetise (soft iron), not mechanically soft.
• Mixing up B and H: B has units T (= Wb m⁻²) while H has units A m⁻¹ — they are different physical quantities related by B = μH for linear media.
• Treating a current loop's magnetic moment vector as scalar — m = IA n̂ where n̂ is the right-hand-rule normal to the loop area.
• Above the Curie temperature ferromagnets become paramagnetic — they do not become diamagnetic.
• Superconductors are perfect diamagnets (χ = −1) — a common appearance in assertion-reason items.

2.5 Key formulas table