as we all konw, we can get the permittivity via the equation that
C=εS/(4πkd) = Q/U
where, C is the Capacity od the dielectric, S & d represent the area & thickness, k is boltzmann constant, Q & U are the charge quantity and the voltage
but since the permittivity is related to the frequency, the relative permittivity shows different values under different frequency
i want to ask, which frequency is the perimittivity we obtain through the equation above related to ?
you will get the materials original dielectric constant (DC). But whenever frequency comes, then it is called effective dielectric constant (EDC). This EDC constant varies with frequency. when frequency increases then it's value reaches from minimum value to original DC.
1 < EDC < DC
Dear Zhonglei Li,
usually frequency is associated to periodic phenomena, such as the steady charging and discharging of a capacitor.
If a capacitor is connected directly to a DC source, the charging process implies a transient, which in practice can be very rapid. During this process the voltage drop across the capacitor rises as V= V0 (1 – e-t/RC), where V0 is the potential of the battery, and RC is the time constant.
To obtain that law for the voltage drop you may solve the following differential equation: R dQ/dt + Q/C = V0. And to solve it, you may deploy a Laplace or Fourier transform.
However, in electrostatics the above process is studied in connection with energy storage in the capacitor, and radiation phenomena are avoided. Thus the charging has to be very slow. I hope this answers your question.
First off should Capacitance C not be simply
C=epsilon Area/ distance ?
Why does Boltzmann's constant make an appearance?
Is complex permittivity perhaps what you need to consider?
I surprised together with P.J. Gregg. The appearance of the Boltzmann constant in the formula for the capacitance - a new word in electrostatics.
Dear Zhonglei Li, if you want to study the dependence of the permittivity from the frequency you have chosen not the best method!
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