Introduction

The previous two sub-topics of this unit built up electrostatics -- the field and potential produced by charges AT REST. This sub-topic turns to what happens once charge is allowed to MOVE: a moving charge, or an electric current (which is simply charge in organised, continuous motion through a conductor), is found to produce an entirely new kind of field around itself -- a magnetic field -- and, in turn, to experience a force whenever it moves through someone else's magnetic field. The chapter opens with Oersted's historic experiment (Section 4.2), which first revealed that electricity and magnetism are not two separate subjects but two faces of one underlying phenomenon, electromagnetism. It then develops the Biot-Savart law (Section 4.3) as the fundamental rule for computing the magnetic field produced by any current distribution, and applies it to two of the most important current geometries: a long straight wire (Section 4.4) and a circular current loop (Section 4.5). Ampere's circuital law (Section 4.6) is then introduced as a powerful shortcut for the same kind of calculation in situations with high symmetry, and is used to re-derive the straight-wire field and to find the field inside a long solenoid (Section 4.7). The chapter then turns around, from field PRODUCTION to field EFFECT: the Lorentz force on a moving charge (Section 4.8), the resulting circular motion of a charged particle in a perpendicular magnetic field and the cyclotron that exploits it (Section 4.9), the force on a current-carrying conductor (Section 4.10), the mutual force between two parallel current-carrying conductors that defines the SI unit ampere itself (Section 4.11), and the torque on a current loop (Section 4.12), which is then put to direct practical use in the moving-coil galvanometer and its conversion into a working ammeter or voltmeter (Sections 4.13-4.14).