## 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.E_{ρ}dv
in which E_{ρ} 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

**Download:** **PDF**

### Submission history

[v1] 10 Aug 2009

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