Magnetism and Matter

This chapter explores the magnetic behavior of matter, starting with the familiar bar magnet. You will learn to model a bar magnet as a magnetic dipole, analogous to an electric dipole, and calculate its magnetic moment, the torque it experiences, and its potential energy in an external magnetic field. The chapter also introduces the concept of a bar magnet being equivalent to a solenoid, which connects the topic to the magnetic effects of current from the previous chapter.

A significant portion is dedicated to the Earth's own magnetic field. You will study its components: the angle of declination, the angle of dip or inclination, and the horizontal component. This section requires careful three-dimensional visualization. The final part classifies materials based on their response to magnetic fields. You will learn about key quantities like magnetic intensity (H), magnetisation (M), magnetic susceptibility (χ), and permeability (μ). Understanding the distinction between these and how they relate to each other is where students often find the chapter challenging. The classification into diamagnetic, paramagnetic, and ferromagnetic materials, along with the hysteresis loop for ferromagnets, concludes the topic.

Formulas for Magnetism and Matter

Torque on a magnetic dipole: $\vec{\tau} = \vec{m} \times \vec{B}$ m is the magnetic dipole moment and B is the external magnetic field.
Potential energy of a magnetic dipole: $U = -\vec{m} \cdot \vec{B}$ The zero of potential energy is usually taken when m is perpendicular to B.
Magnetic field on the axis of a dipole: $B_{\text{axial}} = \frac{\mu_0}{4\pi} \frac{2m}{r^3}$ For a short bar magnet, where r is the distance from the center.
Magnetic field on the equatorial line of a dipole: $B_{\text{equatorial}} = \frac{\mu_0}{4\pi} \frac{m}{r^3}$ For a short bar magnet, where r is the distance from the center.
Angle of dip (or inclination): $\tan \delta = \frac{B_V}{B_H}$ δ is the angle of dip, B_V and B_H are the vertical and horizontal components of Earth's magnetic field.
Magnetisation: $M = \frac{m_{\text{net}}}{V}$ m_net is the net magnetic dipole moment of the material per unit volume V.
Relation between B, H, and M: $\vec{B} = \mu_0 (\vec{H} + \vec{M})$ B is the total magnetic field, H is the magnetic intensity, M is the magnetisation.
Magnetic susceptibility: $M = \chi H$ χ (chi) is a dimensionless quantity. This relation holds for linear materials like para- and diamagnets.
Magnetic permeability: $B = \mu H$ μ is the magnetic permeability of the medium.
Relation between relative permeability and susceptibility: $\mu_r = 1 + \chi$ μ_r is the relative magnetic permeability of the material.