Chapter 5 — Magnetism and Matter
A bar magnet is a solenoid in disguise: its field is a dipole field, its field lines never end, and the way matter responds to a field — weakly against it, weakly with it, or overwhelmingly with it — sorts every material into one of three families.
For nearly a thousand years sailors crossed oceans by trusting a sliver of magnetised iron floating on water. Today a phone finds north with a magnetometer chip smaller than a grain of rice, an MRI scanner maps the water in your brain using a field tens of thousands of times stronger than the Earth's, and every electric car, wind turbine and hard-disk drive depends on permanent magnets made of carefully engineered alloys. Yet a magnet seems mysterious: nothing visible flows, and no battery is attached. Where does its field come from, and why does it pull on iron but not on aluminium?
Chapter 4 showed that electric currents produce magnetic fields and that a current loop behaves like a tiny magnet. This chapter turns the idea round. A bar magnet behaves exactly like a solenoid, because inside it countless atomic current loops are lined up; its far field has the same shape as the field of an electric dipole, and in a uniform field it turns and oscillates like a compass needle. Because there are no isolated magnetic poles, magnetic field lines always close on themselves — Gauss's law for magnetism. Then we look inside materials: the magnetisation they acquire in a field, the magnetic intensity that causes it, and the susceptibility that measures their response — weak and negative for diamagnets, weak and positive for paramagnets, and enormous for ferromagnets such as iron, which can even remember the field they were placed in.
- describe the field of a bar magnet with field lines, explain why it behaves as an equivalent solenoid, and calculate its field on the axial and equatorial lines;
- find the torque on and the potential energy of a magnetic dipole in a uniform field, and use $T=2\pi\sqrt{I/(mB)}$ for an oscillating needle;
- use the analogy between electric and magnetic dipoles, and state and apply Gauss's law for magnetism;
- use magnetisation, magnetic intensity, susceptibility and permeability, including $\mathbf B=\mu_0(\mathbf H+\mathbf M)$;
- classify materials as diamagnetic, paramagnetic or ferromagnetic, explain ferromagnetism with domains, and apply Curie's law and the Curie temperature;
- solve board, JEE Main, JEE Advanced and NEET problems on all of the above.
Sections in this chapter
The Bar Magnet, Magnetic Dipoles and Gauss's Law for Magnetism
Poles and field lines, the bar magnet as an equivalent solenoid, torque, energy and oscillations in a uniform field, the electrostatic analogue and zero magnetic flux through closed surfaces.
Magnetisation, Magnetic Intensity and Magnetic Properties of Materials
$\mathbf M$, $\mathbf H$, susceptibility and permeability; diamagnetism, paramagnetism and Curie's law; ferromagnetism, domains and the Curie temperature.