Q.What happens to the domains in a ferromagnetic material in the presence of an external magnetic field?

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 …