Linear lossy dielectric - wykład

Linear lossy dielectric In some dielectric materials, losses involved in changing the state of polarisation cannot be
entirely neglected. In these materials, we can sometimes write a linear differential equation
relating the polarisation and its time rate of change, and the corresponding quantities for
the electric field. Specification of the amount of energy lost would be possible if we knew
the details of the time variation involved.
When the time variation is sinusoidal , the results admit of a simple description. For a
sinusoidally varying electric field, the resulting polarisation response is also sinusoidal, but
lags a little behind the electric field. This behaviour is described by the phasor equation
P = (χ0
e − jχ00
e ) ²0 E (5.8)
where χ0e and χ00 e are the energy-storage and energy-loss components of a complex
dielectric susceptibility. Please note that although losses are involved, the response is
still linear in that the phasor P is still proportional to the phasor E. The corresponding
description in terms of a complex dielectric permittivity is
D = (²0 − j²00) E (5.9)
It might be noted, by comparing the form of this equation with that of the electrical
conductivity equation appearing is Section 5.2.11, that although the physical mechanisms
might be regarded as being different, the effects of electronic conduction loss and polarisation
loss are, on a macroscopic scale and with sinusoidal excitation, indistinguishable.
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