Simple Nature - Light and Matter

b/A stud finder is used to
locate the wooden beams, or
studs, that form the frame behind
the wallboard. It is a capacitor
whose capacitance changes
when it is brought close to a
substance with a particular
permittivity. Although the wall
is external to the capacitor, a
change in capacitance is still
observed, because the capacitor
has “fringing fields” that extend
outside the region between its
plates.

voltage difference between the plates. If we measureqfree/V, we have

a result that is larger than the capacitance we would have expected.

Although the relationshipE↔qbetween electric fields and their

sources is unalterably locked in by Gauss’s law, that’s not what we

see in practical measurements. In this example, we can measure the

voltage difference between the plates of the capacitor and divide

by the distance between them to find E, and then integrate an

ammeter reading to find qfree, and we will find that Gauss’s law

appears not to hold. We haveE ↔ qfree/(constant), where the

constant fudge factor is greater than one. This constant is a property

of the dielectric material, and tells us how many dipoles there are,

how strong they are, and how easily they can be reoriented. The

conventional notation is to incorporate this fudge factor into Gauss’s

law by defining an altered version of the electric field,

D=E,

and to rewrite Gauss’s law as

ΦD=qin, free.

The constantis a property of the material, known as its permittiv-

ity. In a vacuum,takes on a value known aso, defined as 1/(4πk).

In a dielectric,is greater thano. When a dielectric is present be-

tween the plates of a capacitor, its capacitance is proportional to

(problem 38). The following table gives some sample values of the

permittivities of a few substances.

substance /oat zero frequency

vacuum 1

air 1.00054

water 80

barium titanate 1250

A capacitor with a very high capacitance is potentially a superior

replacement for a battery, but until the 1990’s this was impracti-

cal because capacitors with high enough values couldn’t be made,

even with dielectrics having the largest known permittivities. Such

supercapactors, some with values in the kilofarad range, are now

available. Most of them do not use dielectric at all; the very high

capacitance values are instead obtained by using electrodes that are

not 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 being

completely aligned, this is not a situation commonly encountered

in practice. In such a situation, the material would be as polarized

as it could possibly be, and if the field was increased further, it

would not respond. In reality, a capacitor, for example, would nor-

mally be operated with fields that produced quite a small amount

of alignment, and it would be under these conditions that the linear

736 Chapter 11 Electromagnetism