Q.A rod of magnetic material of cross section 0.25 cm$^2$ is located in a 4000 A m$^{-1}$ magnetising field. The magnetic flux passing through the rod is $25\times10^{-6}$ Wb. Find

Magnetic Susceptibility: The Material's Response to a Magnetic Field

Imagine you place a bar of iron near a magnet. The iron gets magnetized — it becomes a magnet itself. Now imagine you place a piece of wood or copper near the same magnet. Nothing noticeable happens. But something is happening at the atomic level, just much more weakly. Magnetic susceptibility is the number that tells you how much a material magnetizes when you put it in a magnetic field.

The Intuition: A Material's "Magnetic Willingness"

Think of a magnetic field as a push. Some materials push back, some barely respond, and some eagerly align with the push. Susceptibility $\chi$ (chi) is the measure of that eagerness.

If you apply a magnetic field $H$ (the "push"), the material develops a magnetization $M$ (the "response"). The relationship is simple:

So $\chi = M/H$. A large $\chi$ means a small field produces a large magnetization. A zero $\chi$ means the material ignores the field entirely. A negative $\chi$ means the material magnetizes opposite to the field.

The Precise Definition

Magnetic susceptibility is the dimensionless proportionality constant that relates the magnetization $M$ (magnetic dipole moment per unit volume) to the applied magnetic field intensity $H$:

• $M$ is measured in A/m (amperes per meter)
• $H$ is also in A/m
• So $\chi$ has no units — it's a pure number

This is the volume susceptibility. There is also mass susceptibility ($\chi_m = \chi/\rho$, where $\rho$ is density) and molar susceptibility ($\chi_{\text{mol}} = \chi M_{\text{mol}}/\rho$), but the core idea is the same.

What the Sign and Size Tell You

The value of $\chi$ divides all materials into three broad families:

Why Diamagnets Are Negative

Every atom has orbiting electrons. When you apply a magnetic field, those orbits change slightly to produce a tiny magnetic moment that opposes the applied field (Lenz's law at the atomic scale). This happens in all materials, but in diamagnets it's the only effect because the atoms have no permanent magnetic moment. The result is a small negative $\chi$.

Why Paramagnets Are Positive

Some atoms have unpaired electrons, giving them a permanent magnetic moment (like tiny bar magnets). Without an external field, these moments point randomly. When you apply $H$, they partially align with it, producing a net magnetization in the same direction as $H$ — hence positive $\chi$. Thermal jostling fights this alignment, so $\chi$ decreases as temperature rises (Curie's law: $\chi = C/T$).

The Big Picture

Susceptibility is the material's fingerprint in a magnetic field. It tells you:

• Whether the material will be attracted to a magnet (positive $\chi$) or repelled (negative $\chi$)
• How strong that attraction or repulsion will be
• Whether the material can be used for magnetic storage, shielding, or sensing

Magnetic susceptibility is a definition-heavy CBSE Class 12 Physics NCERT topic, commonly searched as magnetic susceptibility formula and types class 12 or diamagnetic paramagnetic ferromagnetic susceptibility values. Because it is the key number that classifies every material's magnetic response, it is tested consistently across CBSE boards and JEE Main/NEET physics.