Introduction

Electricity begins with a simple observation known since antiquity: a piece of amber, rubbed vigorously with fur or cloth, starts to attract small bits of straw, paper or dry leaves. The Greek word for amber, elektron, is the root of every modern word for electricity. It took more than two thousand years, from these first observations to Coulomb's precise force law in 1785 and Gauss's theorem in the early nineteenth century, to turn this curiosity into a complete quantitative theory -- electrostatics, the study of the forces, fields and energy of electric charges that are not moving.

This sub-topic, ELECTRIC CHARGES AND FIELDS, is the first half of WBCHSE Semester III's Unit 1, Electrostatics, and it lays the foundation on which everything else in electricity and magnetism is built. The account proceeds in the order the syllabus lists it:

• Electric charge (Section 1.2) and its three defining properties -- additivity, conservation, and quantisation.
• Coulomb's law (Section 1.3) for the force between two point charges, extended to many charges via the superposition principle (Section 1.4) and to continuous charge distributions described by a charge density (Section 1.5).
• The electric field (Section 1.6), the field created by a point charge, and field lines (Section 1.7), the standard way of picturing a field.
• The electric dipole (Section 1.8): its field on the axis (Section 1.9), on the equatorial line (Section 1.10), at a general point (Section 1.11), and the torque it experiences in a uniform external field (Section 1.12).
• Electric flux (Section 1.13) and Gauss's theorem (Section 1.14), together with its three classic applications -- an infinitely long charged wire (Section 1.15), an infinite charged plane sheet (Section 1.16), and a uniformly charged thin spherical shell (Section 1.17).

These ideas are not merely abstract mathematics. The static shock felt after walking across a carpet, the crackle of a nylon shirt pulled over the head, the roar of a lightning strike, and the operation of photocopiers, laser printers, and the capacitors inside every phone charger, all trace back directly to the physics developed in this sub-topic.