Q.Read the following paragraph and answer the questions given below. Ferromagnetic substances are those which get strongly magnetized when placed in an external magnetic field. They have strong tendency to move from a region of weak magnetic field to strong magnetic field, that is, they get strongly attracted to a magnet. The individual atoms (or ions or molecules) in a ferromagnetic material possess a dipole moment as in a paramagnetic material. However, they interact with one another in such a way that these spontaneously align themselves in a common direction over a macroscopic volume called domain. Each domain has a net magnetization. Typical domain size is 1 mm and the domain contains about 10^11 atoms. In the first instant the magnetization varies randomly from domain to domain and there is no bulk magnetization. When we apply an external magnetic field B0 the domains orient themselves in the direction of B0 and simultaneously that domain oriented in the direction of B0 grows in size. We may wonder as to what happens when the external field is removed, in some ferromagnetic materials the magnetization persists. Such materials are called hard magnetic materials of hard magnets. Alnico, an alloy of iron, aluminium, nickel, cobalt and copper is one such material. There is a class of magnetic materials in which the magnetization disappears on removal of the external field. Soft iron is one such material. Such materials are called soft ferromagnetic materials. There are number of elements which are ferromagnetic. Iron, cobalt, Nickel, gadolinium etc. The ferromagnetic property depends on temperature. At high enough temperature a ferromagnet becomes a paramagnet. That domain structure disintegrates with temperature. This disappearance of magnetization with the temperature is gradual. Questions :

Ferromagnetism: The Intuition

Imagine a room full of tiny compass needles, each free to spin. Normally, they point in random directions — left, right, up, down — so the room as a whole has no net direction. Now walk in with a strong bar magnet. Every needle snaps to point along the magnet's field. But here's the strange part: even after you take the magnet out of the room, most needles stay pointing the same way. The room has "remembered" the field.

That is ferromagnetism in a nutshell. The material doesn't just respond to an external magnetic field — it keeps that response after the field is gone.

The Physics: Why This Happens

Ferromagnetism arises from a quantum-mechanical effect called exchange interaction. In simple terms, the electrons in certain atoms (like iron, cobalt, nickel) have a strong preference to align their spins parallel to each other. This is not a magnetic force in the ordinary sense — it's a purely quantum effect that makes neighbouring atomic magnets want to point the same way.

Because of this, the material spontaneously divides into domains — microscopic regions (typically $10^{-6}$ to $10^{-3}$ m across) where all atomic magnetic moments are already aligned. In an unmagnetised piece of iron, these domains point in different directions, so the net magnetisation is zero.

When you apply an external magnetic field $\vec{B}_0$, the domains that are already aligned with the field grow at the expense of the others. The domain walls move. At high enough fields, all domains merge into one, and the material is saturated — every atomic moment points the same way.

The Key Quantities

The magnetic susceptibility $\chi_m$ for a ferromagnet is enormous — typically $10^3$ to $10^5$, compared to $10^{-5}$ for paramagnets. The relation is:

where $\vec{M}$ is the magnetisation (magnetic moment per unit volume) and $\vec{H}$ is the applied magnetic field intensity. But this $\chi_m$ is not constant — it depends on the history of the material.

Hysteresis: The Memory Effect

When you remove the external field, the domains do not return to random orientations. They get stuck — partly because of impurities and crystal defects that pin the domain walls. The material retains a remanent magnetisation $\vec{M}_r$. To bring it back to zero magnetisation, you must apply a field in the opposite direction, called the coercive field $\vec{H}_c$.

This loop — magnetisation vs. applied field — is called a hysteresis loop. Its area equals the energy lost as heat per cycle (used in transformers, where you want a narrow loop to minimise loss).

The Precise Statement …