structural:reformatting, information:classification
Parallel-plate capacitor

The simplest model of a capacitor consists of two thin parallel conductive plates each with an area of A {\displaystyle A} separated by a uniform gap of thickness d {\displaystyle d} filled with a dielectric of permittivity ε {\displaystyle \varepsilon }. It is assumed the gap d {\displaystyle d} is much smaller than the dimensions of the plates. This model applies well to many practical capacitors which are constructed of metal sheets separated by a thin layer of insulating dielectric, since manufacturers try to keep the dielectric very uniform in thickness to avoid thin spots which can cause failure of the capacitor.

Since the separation between the plates is uniform over the plate area, the electric field between the plates E {\displaystyle E} is constant, and directed perpendicularly to the plate surface, except for an area near the edges of the plates where the field decreases because the electric field lines "bulge" out of the sides of the capacitor. This "fringing field" area is approximately the same width as the plate separation, d {\displaystyle d}, and assuming d {\displaystyle d} is small compared to the plate dimensions, it is small enough to be ignored. Therefore, if a charge of + Q {\displaystyle +Q} is placed on one plate and − Q {\displaystyle -Q} on the other plate (the situation for unevenly charged plates is discussed below), the charge on each plate will be spread evenly in a surface charge layer of constant charge density σ = ± Q / A {\displaystyle \sigma =\pm Q/A} coulombs per square meter, on the inside surface of each plate. From Gauss's law the magnitude of the electric field between the plates is E = σ / ε {\displaystyle E=\sigma /\varepsilon }. The voltage(difference) V {\displaystyle V} between the plates is defined as the line integral of the electric field over a line (in the z-direction) from one plate to another V = ∫ 0 d E (z) d z = E d = σ ε d = Q d ε A {\displaystyle V=\int _{0}^{d}E(z)\,\mathrm {d} z=Ed={\frac {\sigma }{\varepsilon }}d={\frac {Qd}{\varepsilon A}}} The capacitance is defined as C = Q / V {\displaystyle C=Q/V}. Substituting V {\displaystyle V} above into this equation

C = ε A d {\displaystyle C={\frac {\varepsilon A}{d}}}

Therefore, in a capacitor the highest capacitance is achieved with a high permittivity dielectric material, large plate area, and small separation between the plates.

Since the area A {\displaystyle A} of the plates increases with the square of the linear dimensions and the separation d {\displaystyle d} increases linearly, the capacitance scales with the linear dimension of a capacitor (C ∝ L {\displaystyle C\varpropto L}), or as the cube root of the volume.

A parallel plate capacitor can only store a finite amount of energy before dielectric breakdown occurs. The capacitor's dielectric material has a dielectric strength U which sets the capacitor's breakdown voltage at V = V = U d. The maximum energy that the capacitor can store is therefore E = 1 2 C V 2 = 1 2 ε A d (U d d) 2 = 1 2 ε A d U d 2 {\displaystyle E={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(U_{d}d\right)^{2}={\frac {1}{2}}\varepsilon AdU_{d}^{2}}

The maximum energy is a function of dielectric volume, permittivity, and dielectric strength. Changing the plate area and the separation between the plates while maintaining the same volume causes no change of the maximum amount of energy that the capacitor can store, so long as the distance between plates remains much smaller than both the length and width of the plates. In addition, these equations assume that the electric field is entirely concentrated in the dielectric between the plates. In reality there are fringing fields outside the dielectric, for example between the sides of the capacitor plates, which increase the effective capacitance of the capacitor. This is sometimes called parasitic capacitance. For some simple capacitor geometries this additional capacitance term can be calculated analytically. It becomes negligibly small when the ratios of plate width to separation and length to separation are large.

For unevenly charged plates: