Introduction

Thales of Miletus (640 - 548BC) described how a piece of amber, when rubbed, will attract small objects and from this developed the science of electrostatics. Electrostatics decribes the properties of electric charges at rest.

Electricity consists of positive and negative charges with the fundamental property that, like charges repel each other and opposite charges attract. The smallest negative charge is that of the electron (JJ Thomson, 1897) whereas the smallest positive charge has the same magnitude and is found on the proton. The mass of the electron is only $9 \times 10^{-31}kg$ and the proton is 1837 times heavier. The radius of the electron is $3\times 10^{-15}m$ and so charges can be modelled as point charges.

Atoms contain positive and negative charges and are typically $10^{-10}m$ in size. The positive charge is on the proton in the nucleus of the atom and the nucleus consists of both protons and neutrons. The negatively charged electrons move around the nucleus -like planets around the Sun. Normal matter consists of neutral atoms with no excess of positive or negative charges. A cubic metre of a solid contains the order of $10^{29}$ atoms.

A microscopic viewpoint deals with individual particles, whereas a macroscopic approach averages their properties over the large number of atoms and electrons in a tiny volume. A tenth of a milligram contains about $10^{20}$ atoms.

Electric currents are caused by the motion of positive and/or negative charges, for example in a fluorescent tube positive ions move in one direction and electrons in the opposite direction. In metals, such as copper, the charge is carried entirely by electrons. In both cases

• the current = net amount of charge crossing per unit area in unit time.

The direction of the current is the direction of the mean flow of charge.

In an insulator no charge can flow as the electrons are attached to the positive charges. In a conductor, such as a metal, electrolyte or plasma, the positive and negative charges are easily separated so that one or both can move.

Lucretius mentions that certain ores, such as loadstone, attract small pieces of iron by `magnetic forces'. Gilbert realised that the Earth behaves like a large magnet. Later Oersted (1820) and Faraday (1831) showed that the same magnetic effects are produced by currents as by permanent magnets. Then, Ampère suggested that each atom is a tiny electric current (thus a magnet is created if there are electrons moving in different directions which do not cancel). If each atom is magnetic they may be arranged either randomly to make a non-magnetic substance or with the majority in one direction to give a permanent magnet.