Equivalent Circuit Description of Linear Dielectrics

The application of a sinusoidal voltage , V = Vq exp iut, to an ideal dielectric, i.e., one without losses, will result in a charging current (see Prob. 14.1) given by 

Written in terms of the refractive index n = this relation is known as the Lorentz-Lorenz relation. Since electromagnetic radiation, if one ignores the magnetic component, is nothing but a time-varying electric field, it should come as no surprise later, in Chap. 16. when it is discovered that the dielectric and optical responses of insulators are intimately related. 

Remember = cosu -(- isino , where uj is the angular frequency in units of radians per second. To convert to hertz, divide by 27t, since a = Ini/, where ly is the frequency in hertz 

In other words, the resulting current will be tt/2 rad or 90 out of phase from the applied field, which implies that the oscillating charges are in phase with the applied voltage. 

As noted above, Eq. (14.17) is only valid for an ideal dielectric. In reality, the charges are never totally in phase for two reasons (I) the dissipation of energy due to the inertia of the moving species and (2) the long-range hopping of charged species, i.e., ohmic conduction. The total current is thus the vectorial sum of /chg and or 

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