Magnetism and Matter — NEET Notes

The bar magnet — properties and field lines

Sprinkle iron filings on a sheet of glass placed over a short bar magnet and the filings arrange themselves into curves that trace the magnetic field. The pattern reveals two regions of intense activity at the ends — the poles — and a quieter middle. When the magnet is suspended freely, one pole turns toward geographic north (the north pole) and the other toward geographic south (the south pole). Like poles repel, unlike poles attract, and no matter how many times you slice a bar magnet, you never obtain an isolated north or south pole. The simplest specimen that produces a magnetic field is always a magnetic dipole.

The curves traced by iron filings are magnetic field lines. They obey four rules that NEET tests directly. First, the tangent to a field line at any point gives the direction of the net field B there. Second, the density of lines crossing a unit area perpendicular to the field measures the strength of B. Third, magnetic field lines never intersect — if they did, the field direction at the crossing would be ambiguous. Fourth, and most distinctively, magnetic field lines form continuous closed loops: outside the magnet they run from north to south, and inside the material they continue from south back to north. This is unlike electric field lines, which begin on positive charges and end on negative ones.

The resemblance between a bar magnet and a current-carrying solenoid is so close that NCERT formalises it as an equivalence. Move a compass needle around either, and you cannot tell them apart. Calculate the far axial field of a finite solenoid and you recover the far axial field of a bar magnet — same dependence on distance, same dipole structure. Ampere's hypothesis, made before the discovery of the electron, turned out to be exactly right: every magnetic moment in nature, including the moment of a permanent magnet, ultimately arises from circulating charges. In a bar magnet the circulation is invisible — it lives at the atomic scale, in the orbital and spin motion of electrons.

Magnetic dipole moment

The strength of a bar magnet is captured by a single vector quantity, the magnetic dipole moment m. Treating the magnet as a pair of magnetic poles of strength q_m separated by a distance 2L (the magnetic length), the moment is defined as

m = q_m × 2L

Magnitude of the magnetic dipole moment

The direction of m is from the south pole to the north pole inside the magnet. The SI unit is A m². For a current loop of area A carrying current I, the corresponding result from the previous chapter is m = NIA, with N turns; for a solenoid of length L, cross-section A, n turns per metre, carrying current I, the moment becomes m = nLAI. These two expressions — pole-times-length and current-times-area — measure the same physical quantity from two different angles. Either can be used in NEET problems, and the choice usually depends on what data the question hands you.

Torque on a magnetic dipole

Drop a magnet into a uniform external field and the field grabs hold of it. Because both poles experience equal and opposite forces (the field is uniform), the net force is zero — the magnet does not translate. But there is a couple that rotates it. The result, identical in form to the torque on an electric dipole in an electric field, is

τ = m × B   |τ| = mB sin θ

Torque on a dipole in a uniform field

Here θ is the angle between m and B. The torque is maximum when m is perpendicular to B and zero when the two are parallel or anti-parallel. The torque is restoring: it always tries to bring the dipole into alignment with the field, in the same way that the electric force tries to align an electric dipole with the field. Integrating −τ dθ gives the potential energy stored in the orientation,

U = −m·B = −mB cos θ

which is minimum (U = −mB) when θ = 0° — the stable equilibrium with the dipole aligned along the field — and maximum (U = +mB) when θ = 180°, the unstable equilibrium with the dipole anti-parallel. At θ = 90° the energy is zero (by convention). To rotate a dipole from θ₁ to θ₂ an external agent must do work W = mB(cos θ₁ − cos θ₂), and this is a NEET workhorse.

One subtlety NEET likes to probe: a magnet in a non-uniform field experiences a net force in addition to torque. An iron nail near a bar magnet is attracted because the bar's field is stronger at the nail's near end than at its far end, producing a net pull. In a strictly uniform field, the force on the dipole is identically zero — only a torque exists.

Field of a bar magnet — axial and equatorial

At large distances from the magnet (r ≫ L), the magnetic field is given by formulas that exactly parallel the electric field of a dipole, with the substitutions E → B, p → m, and 1/(4πε₀) → μ₀/(4π).

The fundamental physical scaling is the inverse-cube law, which holds because a dipole's two opposite sources nearly cancel at large distances and only the residual difference survives. This is the same reason the gravitational tidal field of the Moon falls as 1/r³, not 1/r². For a NEET problem, three numbers are usually enough: identify whether the point lies on the axis or the equator, plug into the appropriate expression, and assign direction using the dipole-moment vector.

Gauss's law for magnetism

The most profound statement in this chapter is also the shortest. Pick any closed surface, anywhere in space, and add up the magnetic flux through it. The answer is always zero.

∮ B · dA = 0

Gauss's law for magnetism — there are no magnetic monopoles

Compare with the electric version, where the closed-surface flux equals the enclosed charge divided by ε₀. The fact that the magnetic version always returns zero — no matter what magnets, currents, or arrangements you enclose — is a direct statement that isolated magnetic charges do not exist. Every magnetic field line that enters a closed surface must also leave it, because every line ultimately forms a closed loop. There are no sources of B and no sinks of B. The simplest magnetic element is, and always will be, a dipole.

NEET 2023 asked this in one line: The net magnetic flux through any closed surface is — (1) negative (2) zero (3) positive (4) infinity. The answer is (2), and the reason every aspirant needs to be able to state is "because magnetic monopoles do not exist." Worth knowing too: if hypothetical monopoles of magnetic charge q_m were discovered, the right-hand side of Gauss's law would become μ₀q_m, mirroring the electric version exactly. They have been searched for for decades. They have never been found.

Earth's magnetism — declination, dip, horizontal component

Earth itself is a magnet. The magnetic field at the surface points roughly from geographic south to geographic north (so the magnetic south pole of the Earth's giant internal "magnet" sits near the geographic north). The molten outer core, swirling under convection, generates this field through a self-sustaining dynamo. NCERT and NIOS describe three measurable quantities — the elements of Earth's magnetic field — that any aspirant must know.

From the three components a compass needle resolves the rest. NEET 2017 set a classic on this: if θ₁ and θ₂ are the apparent dips measured in two vertical planes at right angles to each other, then the true dip θ satisfies cot²θ = cot²θ₁ + cot²θ₂. The derivation hinges on noticing that the horizontal component of the field along a tilted plane is shortened by the cosine of the angle between that plane and the magnetic meridian, while the vertical component is unchanged. Aspirants should memorise the final relation but be able to re-derive it from B_V/B_H.

Magnetisation and magnetic intensity

So far we have treated the magnet as a finished object. In Section 5.4 of NCERT — and this is the conceptual heart of the chapter — we ask how matter becomes magnetised in the first place. A bulk material is made of atoms, and each atom carries a tiny circulating-current magnetic moment from its orbital and spin electron motion. When these atomic moments add up vectorially over a unit volume, the result is the magnetisation.

M = m_net / V

Magnetisation: net magnetic moment per unit volume (A m⁻¹)

Now place a long solenoid carrying current I with n turns per metre, producing a vacuum field B₀ = μ₀nI. If you fill the solenoid with a magnetic material, the atomic dipoles inside align with B₀ and contribute their own field, B_m = μ₀M. The total field is

B = B₀ + B_m = μ₀(H + M)

where the auxiliary vector H = B/μ₀ − M is called the magnetic intensity (or magnetising field). Crucially, H measures only the externally driven part of the field — it depends on the free currents in the solenoid windings, but not on the bound currents inside the magnetised material. M measures only the material's response. The total field B combines both contributions. Both H and M have units of A m⁻¹.

Susceptibility, permeability, and the linear regime

For most materials at modest field strengths, the magnetisation responds linearly to the applied intensity:

M = χ_m H

Linear constitutive relation: χ_m is the magnetic susceptibility

The dimensionless number χ_m is a fingerprint of the material — a tiny negative number for diamagnets, a small positive number for paramagnets, and a huge positive number for ferromagnets. Substituting into B = μ₀(H + M) gives B = μ₀(1 + χ_m)H = μH, where

μ = μ₀(1 + χ_m) = μ₀ μ_r

μ is the absolute permeability of the substance and μ_r = 1 + χ_m is the dimensionless relative permeability — the magnetic analog of the dielectric constant. Given any one of χ_m, μ_r, or μ, the other two follow immediately. NEET 2020 made aspirants compute exactly this: an iron rod has χ_m = 599, so μ_r = 600, and μ = 600 × 4π × 10⁻⁷ T m A⁻¹ ≈ 2.4 × 10⁻⁴ T m A⁻¹. Such "plug-and-evaluate" questions are gifts; an aspirant who knows the three-quantity relation cannot miss them.

Magnetic properties of materials — dia, para, ferro

The sign and magnitude of χ_m partitions every substance in nature into one of three families. The boundaries are sharp, and NEET tests them every other year. The table below is borrowed from NCERT Section 5.5 and committed to memory by every serious aspirant.

It is helpful to compare paramagnetism and ferromagnetism side by side, because both are positive-χ phenomena and both have permanent atomic moments — but they behave very differently because of one extra ingredient.

The signature of a ferromagnet is the domain. Within a domain — typically about a millimetre across, containing ~10¹¹ atoms — exchange interactions force every atomic moment into the same direction. In an unmagnetised piece of iron the domains point every which way and cancel; when an external field is applied, domains aligned with the field grow at the expense of those that are not, and the bulk acquires a strong net magnetisation. Heat the sample, and at the Curie temperature the thermal energy disrupts the exchange order, the domains dissolve, and the material becomes paramagnetic. For iron, this transition occurs at about 1043 K (770 °C). NCERT also reminds us of Curie's law for the paramagnetic regime, χ_m = C/T, where C is the Curie constant. The same law re-emerges for a ferromagnet above its Curie point.

The hysteresis loop — ferromagnetic memory

Drive a ferromagnetic sample through one full cycle of magnetising field and the magnetisation does not retrace its path. The curve of B (or M) versus H traces out a closed loop — the hysteresis loop — that encodes the material's history. The shape of this loop tells you whether a sample is fit to be a permanent magnet (high retentivity, high coercivity — like alnico or steel) or fit to be the core of a transformer (low retentivity, low coercivity — like soft iron).

The area enclosed by the hysteresis loop is the energy dissipated per unit volume per cycle — heat lost to the lattice as domains reorient. Soft magnetic materials (transformer cores) have thin loops because we do not want energy lost every AC cycle. Hard magnetic materials (compass needles, refrigerator magnets) have fat loops because we want the magnetisation to survive after the magnetising field is removed. Retentivity and coercivity together define the personality of a ferromagnet, and NEET routinely asks which property determines what.

Where the energy goes — diamagnet pushed up

One particularly elegant NEET 2018 question places a thin diamagnetic rod vertically between the poles of an electromagnet. Switch on the current and the diamagnet is pushed up, out of the horizontal field, and so gains gravitational potential energy. Where does that energy come from? Not from the magnetic field itself — the magnetic force does no work on moving charges (it is always perpendicular to velocity). Not from the lattice of the rod — the lattice is mechanically passive. The energy comes from the current source: as the diamagnet is expelled, the flux through the electromagnet's coil falls, an opposing emf is induced, and the source must do extra electrical work to maintain the current. That extra work shows up as the rod's increased gravitational potential energy. This single mechanism — energy supplied by the source, mediated by induced emf — is a beautiful bridge between Chapter 5 and the next chapter on electromagnetic induction.