Q.18 Define magnetization. State its S.I. unit and dimensions. What is the relation between permeability and magnetic susceptibility?
Best answer
Answer: Magnetization is the net magnetic dipole moment per unit volume of a material; S.I. unit A/m; dimensions \([L^{-1}A]\) i.e. \([M^0L^{-1}T^0A^1]\); \(\mu = \mu_0(1 + \chi)\) or \(\mu_r = 1 + \chi\).
Magnetization (\(M_z\)): When a material is placed in a magnetising field, its atomic dipoles align and it acquires a net magnetic moment. The net magnetic dipole moment developed per unit volume is called the magnetization:
\[M_z = \frac{m_{\text{net}}}{V}\]S.I. unit: A m\(^2\)/m\(^3\) = A/m (ampere per metre). Dimensions: \([M^0L^{-1}T^0A^1]\).
Relation: Magnetic induction \(B = \mu_0(H + M_z) = \mu_0(H + \chi H) = \mu_0(1+\chi)H\). Since \(B = \mu H\),
\[\mu = \mu_0(1 + \chi)\quad\text{or}\quad \mu_r = \frac{\mu}{\mu_0} = 1 + \chi\]where \(\chi = M_z/H\) is the magnetic susceptibility.
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