Magnetisation, Magnetic Intensity and Susceptibility

For problems: identify whether M, H, B, chi, volume, or dipole moment is given; choose M = m_net/V, chi = M/H, or B = mu0(H + M); keep M and H in A m^-1; check whether chi should have a unit; state what the sign of chi implies.

A conceptual diagram may show a material specimen in an applied magnetic field H, with small dipoles partly aligned, producing magnetisation M. For formula questions, a diagram is helpful but not essential.

Writing susceptibility in A m^-1 is wrong. Susceptibility has no unit because it is the ratio of M to H.

Magnetisation M is the magnetic dipole moment per unit volume of a material. Magnetic intensity H represents the magnetising field, and magnetic susceptibility chi measures how strongly a material becomes magnetised in response to H.

Magnetisation M is the magnetic dipole moment per unit volume of a material. Magnetic intensity H represents the magnetising field, and magnetic susceptibility chi measures how strongly a material becomes magnetised in response to H. Key formulas: M = m_net/V, where M is magnetisation in A m^-1, m_net is net magnetic dipole moment in A m^2, and V is volume in m^3. B = mu0(H + M), where B is magnetic field in tesla, mu0 is permeability of free space, and H and M are in A m^-1. chi = M/H for linear materials, where chi is dimensionless. Use these relations for material-response questions under ordinary school-level linear assumptions unless non-linear ferromagnetic behaviour is specifically mentioned. If a material has M = 120 A m^-1 when H = 400 A m^-1, then chi = M/H = 120/400 = 0.30. The positive value indicates that magnetisation is in the same direction as the magnetising field.

When a material is placed in a magnetic field, its atomic or molecular magnetic dipoles respond to the field. The net magnetic dipole moment per unit volume is called magnetisation M. Magnetic intensity H is used to describe the applied magnetising effect, while the magnetic field inside the material is related to both H and M by B = mu0(H + M). For a linear magnetic material, susceptibility is chi = M/H, so the sign and magnitude of chi tell whether the material is weakly repelled, weakly attracted, or strongly attracted by a magnetic field. Key formulas: M = m_net/V, where M is magnetisation in A m^-1, m_net is net magnetic dipole moment in A m^2, and V is volume in m^3. B = mu0(H + M), where B is magnetic field in tesla, mu0 is permeability of free space, and H and M are in A m^-1. chi = M/H for linear materials, where chi is dimensionless. Use these relations for material-response questions under ordinary school-level linear assumptions unless non-linear ferromagnetic behaviour is specifically mentioned. A sample of volume 2.0 x 10^-5 m^3 has net magnetic dipole moment 6.0 x 10^-3 A m^2 in an applied magnetic intensity of 1.5 x 10^3 A m^-1. Find M and chi. Calculation: M = m_net/V = (6.0 x 10^-3)/(2.0 x 10^-5) = 3.0 x 10^2 A m^-1. chi = M/H = (3.0 x 10^2)/(1.5 x 10^3) = 0.20. Interpretation: the positive susceptibility means the magnetisation is along the applied field. This is commonly tested through definitions, unit-based questions, formula substitution, and comparison questions where susceptibility is used to classify magnetic materials. Writing susceptibility in A m^-1 is wrong. Susceptibility has no unit because it is the ratio of M to H.