Electricity Constants

[Pavido Scalf]

Itis a measure of how dense of an electric field is "permitted" to form in response to electric charges and relates the units for electric charge to mechanical quantities such as length and force.[2] For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law:

The ampere was redefined by defining the elementary charge as an exact number of coulombs as from 20 May 2019,[4] with the effect that the vacuum electric permittivity no longer has an exactly determined value in SI units. The value of the electron charge became a numerically defined quantity, not measured, making μ0 a measured quantity. Consequently, ε0 is not exact. As before, it is defined by the equation ε0 = 1/(μ0c2), and is thus determined by the value of μ0, the magnetic vacuum permeability which in turn is determined by the experimentally determined dimensionless fine-structure constant α:

Historically, the parameter ε0 has been known by many different names. The terms "vacuum permittivity" or its variants, such as "permittivity in/of vacuum",[8][9] "permittivity of empty space",[10] or "permittivity of free space"[11] are widespread. Standards organizations also use "electric constant" as a term for this quantity.[12][13]

Another historical synonym was "dielectric constant of vacuum", as "dielectric constant" was sometimes used in the past for the absolute permittivity.[14][15] However, in modern usage "dielectric constant" typically refers exclusively to a relative permittivity ε/ε0 and even this usage is considered "obsolete" by some standards bodies in favor of relative static permittivity.[13][16] Hence, the term "dielectric constant of vacuum" for the electric constant ε0 is considered obsolete by most modern authors, although occasional examples of continuing usage can be found.

As indicated above, the parameter ε0 is a measurement-system constant. Its presence in the equations now used to define electromagnetic quantities is the result of the so-called "rationalization" process described below. But the method of allocating a value to it is a consequence of the result that Maxwell's equations predict that, in free space, electromagnetic waves move with the speed of light. Understanding why ε0 has the value it does requires a brief understanding of the history.

The experiments of Coulomb and others showed that the force F between two, equal, point-like "amounts" of electricity that are situated a distance r apart in free space, should be given by a formula that has the form

where Q is a quantity that represents the amount of electricity present at each of the two points, and ke depends on the units. If one is starting with no constraints, then the value of ke may be chosen arbitrarily.[17] For each different choice of ke there is a different "interpretation" of Q: to avoid confusion, each different "interpretation" has to be allocated a distinctive name and symbol.

The unit of Gaussian charge, the statcoulomb, is such that two units, at a distance of 1 centimetre apart, repel each other with a force equal to the cgs unit of force, the dyne. Thus, the unit of Gaussian charge can also be written 1 dyne1/2 cm. "Gaussian electric charge" is not the same mathematical quantity as modern (MKS and subsequently the SI) electric charge and is not measured in coulombs.

In order to establish the numerical value of ε0, one makes use of the fact that if one uses the rationalized forms of Coulomb's law and Ampre's force law (and other ideas) to develop Maxwell's equations, then the relationship stated above is found to exist between ε0, μ0 and c0. In principle, one has a choice of deciding whether to make the coulomb or the ampere the fundamental unit of electricity and magnetism. The decision was taken internationally to use the ampere. This means that the value of ε0 is determined by the values of c0 and μ0, as stated above. For a brief explanation of how the value of μ0 is decided, see Vacuum permeability.

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The electric effect of compressing amorphous dielectrics was determined by pressing two kinds of sheet rubber, of dielectric constants 2.94 and 3.96, against seven hard materials, whose dielectric constants ranged from 2.8 to 7.8. The charge on the compressible dielectric was found to be independent of the nature of the material against which it was pressed, proving that this is not a voltaic effect and that amorphous as well as crystalline substances can be electrified by pressure.

The electric effect of collision of a solid insulator and a metal was found, with four pairs of materials, to be consistently opposite in sign to the frictional effect. This result shows that collision must be considered to produce two different effects, one of which is the voltaic charge, while the other is a transfer of electrons from the metal to the dielectric, due in all probability to the inertia of the mobile electrons.

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Recently, hydrovoltaic technology emerged as a novel renewable energy harvesting method, which dramatically extends the capability to harvest water energy. However, the urgent issue restricting its device performance is poor carrier transport properties of the solid surface if large charged interface is considered simultaneously. Herein, a hydrovoltaic device based on silicon nanowire arrays (SiNWs), which provide large charged surface/volume ratio and excellent carrier transport properties, yields sustained electricity by a carrier concentration gradient induced by evaporation-induced water flow inside nanochannels. The device can yield direct current with a short-circuit current density of over 55 μA cm-2 , which is three orders larger than a previously reported analogous device (approximately 40 nA cm-2 ). Moreover, it exhibits a constant output power density of over 6 μW cm-2 and an open-circuit voltage of up to 400 mV. Our finding may pave a way for developing energy-harvesting devices from ubiquitous evaporation-driven internal water flow in nature with semiconductor material of silicon.

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