71002

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 ratę 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. Fora

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 = (Xo

e-jx°°

e) ²oE (5.8)

where xoeand xooeare the energy-storage and energy-loss components of a complex

dielectric susceptibility. Please notę 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 = (²o- j²oo) 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 scalę and with sinusoidal excitation, indistinguishable.