By André Moliton (auth.)
Applied Electromagnetism and Materials selections up the place the author's Basic Electromagnetism and Materials left off by way of providing useful and appropriate technological information regarding electromagnetic fabric houses and their purposes. This ebook is aimed toward senior undergraduate and graduate scholars in addition to researchers in fabrics technological know-how and is the fabricated from a long time of educating simple and utilized electromagnetism. issues variety from the spectroscopy and characterization of dielectrics and semiconductors, to non-linear results and electromagnetic cavities, to ion-beam purposes in fabrics science.
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Additional info for Applied Electromagnetism and Materials
The exercise also can be used to reproduce Eq. 1). The term exp(-2PBAt) in Eqs. (7) and (7') represents a transition regime due to the delay (dephasing) between electrons trapped in potential wells, or dipoles, in following the applied field. As this term varies exponentially with time it is characteristic of the relaxation of the system. It is also a function of the macroscopic relaxation (Y(t)) which is defined in Chapter 3. The double-well potential model thus represents a relaxation, much as that found through Debye's theory, and gives rise to the same types of dielectric equations (Debye equations).
Applied electromagnetism and materials 16 By substituting Eqs. (3) and (4) into Eq. (2), we obtain: d(N B N A ) dt 2PBA (N B N A ) 2PBA qaE 2kT N. The integration of the differential equation without the second term yields: NB – NA = C exp(-2PBAt). By transferring this into the differential equation and by varying the constant denoted C, we obtain: qaE N exp(2PBA t) K . 2kT By using the limiting condition, as in when t = 0, NA = NB = N/2, it is possible to qaE deduce that K N , and from which: 2kT C NB NA N qaE 2 kT (1 exp[2PBA t]) .
Chapter 1. Dielectrics under varying regimes: relaxation phenomena 19 By denoting the number of molecules per unit volume as N, this also being the number of dipoles per unit volume, at a time t = 0 (from when E is applied) we have NA = NB = N/2, and in place of Eq. (5) we can state that N pE NB NA 2 kT (1 exp[2PBA t]) . (5’) The polarization, or rather the resultant dipole moment per unit volume, is thus given by P = (NB – NA)p, and once again Eq. (7) yields Eq. (7') (see preceding paragraph).