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Inductance: Loop and Partial by CLAYTON R. PAUL

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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):

(1.6)images/c03_image001.jpg

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

(1.7)images/c03_image002.jpg

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 ...

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