TABLE OF CONTENTS Magnetostatics deals with stationary currents. So far we considered only static charges. A current, however, consists of moving charges. The fundamental observation, that magnetic fields exist in the neighbourhood of currents, and hence of moving charges, was made by Oersted in 1819. Oersted had observed that a magnetic needle aligns itself in the vicinity of a current carrying wire perpendicular to this wire. Within a very short time after this discovery (i.e. within a few years) Amp re published his results of a series of experiments which established the law of the force today named after him, and Biot and Savart observed the corresponding law (for a current element) that carries their names today. We are concerned with these laws in this chapter.
Here by current density we mean only that of the conduction electrons; we do not mean the current density of (classically considered) circular currents of molecular electrons (which, by the way, are not even sufficiently well known). First we consider the case without matter effects. A precisely known current density j is defined by the charge density of positive charges multiplied by their velocity, i.e.
in ampere/m 2 or C/m 2 s. We use ds for an element of the trajectory or path as indicated in Fig. 5.1, in order not to confuse this with the element of some distance, dr, or the volume element d r. As usual t represents...
