Q.A plate of magnetic material of size 10 cm $\times$ 0.5 cm $\times$ 0.2 cm (length, breadth and thickness respectively) is located in a magnetising field of $0.5\times10^4$ A m$^{-1}$. A magnetic moment of 0.5 A m$^2$ is induced in it. Find the magnetic induction in the plate.

Magnetization M is defined as the net atomic magnetic dipole moment of a material per unit volume, $M=\dfrac{m_{net}}{V}$; it is a vector quantity with SI unit A m$^{-1}$. When a material rod is placed inside a current-carrying solenoid (n turns per unit length, current I), the field produced by the solenoid ALONE is $B_0=\mu_0nI$, and the material contributes an additional field $B_m=\mu_0M$ proportional to its magnetization, so the total field is $B=\mu_0(nI+M)$.

To isolate the part of this that depends only on the solenoid (not on the material placed inside), the magnetic field intensity is defined as $H=nI$, giving $B=\mu_0(H+M)$ -- H and M share the same unit and dimensions, and the total field B inside the material depends on both. This framework -- separating the "driving" field H (set entirely by the external current) from the material's own response M -- is the basis for defining susceptibility and permeability, and for describing how differently dia-, para-, and ferromagnetic materials each respond to the same applied H.