Condensed Matter


Independence of Capacitance from Dielectric

Authors: Hamid V. Ansari

It is shown that there exists a uniqueness theorem, stating that the charges given to a constant configuration of conductors take a unique distribution, which contrary to what is believed does not have any relation to the uniqueness theorem of electrostatic potential. Using this theorem we obtain coefficients of potential analytically. We show that a simple carelessness has caused the famous formula for the electrostatic potential to be written as U = 1/2 ∫D.Edv while its correct form is U = 1/2 ∫D.Eρdv in which Eρ is the electrostatic field arising only from the external charges not also from the polarization charges.
Considering the above-mentioned material it is shown that, contrary to the current belief, capacitance of a capacitor does not at all depend on the dielectric used in it and depends only on the configuration of its conductors. We proceed to correct some current mistakes resulted from the above-mentioned mistakes, eg electrostatic potential energy of and the inward force exerted on a dielectric block entering into a parallel-plate capacitor are obtained and compared with the wrong current ones.
It is shown that existence of dielectric in the capacitor of a circuit causes attraction of more charges onto the capacitor because of the polarization of the dielectric. Then, in electric circuits we should consider the capacitor's dielectric as a source of potential not think wrongly that existence of dielectric changes the capacitor's capacitance. Difference between these two understandings are verified completely during some examples, and some experiments are proposed for testing the theory. For example it is shown that contrary to what the current theory predicts, resonance frequency of a circuit of RLC will increase by inserting dielectric into the capacitor (without any change of the geometry of its conductors). It is also shown that what is calculated as K (dielectric constant) is in fact 2 - (1/K).

Comments: 30 pages

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Submission history

[v1] 10 Aug 2009

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