Magnetic fields due to electrical circuits

Abstract

Consider the stationary current element, that is of length dl and is at the position r _s in Figure 6.1. The field point P is a the position r at a distance R = (r − r _s ) from the current element. We shall determine the contribution to the magnetic field at the field point P, at the time of observation t, due to the moving classical point charges that were passed and counted by the information collecting sphere inside the current element at the retarded time t* = (t − R/c). We shall assume that, when they are counted at the fixed time t*, there are N ₀ moving classical point charges per metre length inside the current element, each of charge q and all moving with the same velocity [u] and the same acceleration [a]. Since we shall find that there are differences in the higher order terms in β between positive and negative moving charges we shall consider both cases, starting with moving positive charges as shown in Figure 6.1. We shall assume that N ₀ is so large that the fluctuations in the number of moving charges inside the current element can be neglected.