Summary

1. The science of magnetism is old. It has been known since ancient times that magnetic materials tend to point in the north-south direction; like magnetic poles repel and unlike ones attract; and cutting a bar magnet in two leads to two smaller magnets. Magnetic poles cannot be isolated.
2. When a bar magnet of dipole moment m is placed in a uniform magnetic field B,
   1. the force on it is zero
   2. the torque on it is m × B,
   3. its potential energy is –m . B, where we choose the zero of energy at the orientation when m is perpendicular to B.
3. Consider a bar magnet of size l and magnetic moment m, at a distance r from its mid-point, where r >>l, the magnetic field B due to this bar is, \[ \begin{aligned} \mathbf{B} &=\frac{\mu_{0} \mathbf{m}}{2 \pi r^{3}} \quad \text { (along axis) } \\ &=-\frac{\mu_{0} \mathbf{m}}{4 \pi r^{3}} \quad \text { (along equator) } \end{aligned} \]
4. Gauss’s law for magnetism states that the net magnetic flux through any closed surface is zero \[ \phi_{B}=\sum_{\text {all area } \atop \text { elements } \Delta \mathrm{s}} \mathbf{B} \cdot \Delta \mathbf{S}=0 \]
5. The earth’s magnetic field resembles that of a (hypothetical) magnetic dipole located at the centre of the earth. The pole near the geographic north pole of the earth is called the north magnetic pole. Similarly, the pole near the geographic south pole is called the south magnetic pole. This dipole is aligned making a small angle with the rotation axis of the earth. The magnitude of the field on the earth’s surface ≈ \(4 × 10^{–5} T\)
6. Three quantities are needed to specify the magnetic field of the earth on its surface – the horizontal component, the magnetic declination, and the magnetic dip. These are known as the elements of the earth’s magnetic field.
7. Consider a material placed in an external magnetic field \(B_{0}\) . The magnetic intensity is defined as, \[ \mathbf{H}=\frac{\mathbf{B}_{0}}{\mu_{0}} \] The magnetisation M of the material is its dipole moment per unit volume. The magnetic field B in the material is, \[ \mathbf{B}=\mu_{0}(\mathbf{H}+\mathbf{M}) \]
8. For a linear material M = χ H. So that B = µ H and χ is called the magnetic susceptibility of the material. The three quantities, χ , the relative magnetic permeability µ r , and the magnetic permeability µ are related as follows: \[ \begin{array}{l} \mu=\mu_{0} \mu_{r} \\ \mu_{r}=1+\chi \end{array} \]
9. Magnetic materials are broadly classified as: diamagnetic, paramagnetic, and ferromagnetic. For diamagnetic materials χ is negative and small and for paramagnetic materials it is positive and small. Ferromagnetic materials have large χ and are characterised by non-linear relation between B and H. They show the property of hysteresis.
10. Substances, which at room temperature, retain their ferromagnetic property for a long period of time are called permanent magnets.