Q.The relation between magnetic susceptibility χ and relative permeability μr of a magnetic material is :

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 …