Simple Nature - Light and Matter

voltage difference between the plates. If we measure q free /V , we havea result that is larger than the capacitance we would have expected.Although the relationship E ↔ q between electric fields and theirsources is unalterably locked in by Gauss’s law, that’s not what wesee in practical measurements. In this example, we can measure thevoltage difference between the plates of the capacitor and divideby the distance between them to find E, and then integrate anammeter reading to find q free , and we will find that Gauss’s lawappears not to hold. We have E ↔ q free /(constant), where theconstant fudge factor is greater than one. This constant is a propertyof the dielectric material, and tells us how many dipoles there are,how strong they are, and how easily they can be reoriented. Theconventional notation is to incorporate this fudge factor into Gauss’slaw by defining an altered version of the electric field,and to rewrite Gauss’s law asD = ɛE ,Φ D = q in, free .The constant ɛ is a property of the material, known as its permittivity.In a vacuum, ɛ takes on a value known as ɛ o , defined as 1/(4πk).In a dielectric, ɛ is greater than ɛ o . When a dielectric is present betweenthe plates of a capacitor, its capacitance is proportional to ɛ(problem 38). The following table gives some sample values of thepermittivities of a few substances.substance ɛ/ɛ o at zero frequencyvacuum 1air 1.00054water 80barium titanate 1250A capacitor with a very high capacitance is potentially a superiorreplacement for a battery, but until the 1990’s this was impracticalbecause capacitors with high enough values couldn’t be made,even with dielectrics having the largest known permittivities. Suchsupercapactors, some with values in the kilofarad range, are nowavailable. Most of them do not use dielectric at all; the very highcapacitance values are instead obtained by using electrodes that arenot parallel metal plates at all, but exotic materials such as aerogels,which allows the spacing between the “electrodes” to be very small.Although figure a/2 shows the dipoles in the dielectric beingcompletely aligned, this is not a situation commonly encounteredin practice. In such a situation, the material would be as polarizedas it could possibly be, and if the field was increased further, itwould not respond. In reality, a capacitor, for example, would normallybe operated with fields that produced quite a small amountof alignment, and it would be under these conditions that the linearb / A stud finder is used tolocate the wooden beams, orstuds, that form the frame behindthe wallboard. It is a capacitorwhose capacitance changeswhen it is brought close to asubstance with a particularpermittivity. Although the wallis external to the capacitor, achange in capacitance is stillobserved, because the capacitorhas “fringing fields” that extendoutside the region between itsplates.Section 11.7 Electromagnetic Properties of Materials 709