3

FIELDS OF TIME-VARYING CURRENTS (ACCELERATED CHARGE)

In Chapter 2 we investigated the calculation of the magnetic fields produced by various configurations of static (dc) currents (the *steady* flow of charge). We discussed in Chapter 1 how the inductance of a structure will be obtained from these static magnetic fields by first obtaining the magnetic flux penetrating the surface of the current loop from (1.6):

and then obtaining the inductance of the loop from (1.7):

This inductance parameter will then be used in lumped circuits to determine its effect in circuits in which the currents vary with time (*accelerated* charge). The electromagnetics law that allows this determination is Faraday’s law of induction. However, we seem to have a logical inconsistency in this process: A circuit element, inductance, that was derived for static (dc) currents will be used to evaluate its effect on time-varying currents. The ability to use a result derived for dc currents in a situation where the currents vary with time is shown in Section 3.4 to be a valid approximation using an iterative solution of the field equations. This approximation will be valid for circuits whose maximum dimensions are “electrically small,” that is, much less than a wavelength at the frequency of the driving ...