We could investigate this question experimentally. Suppose that we started with a charged parallel plate capacitor, whose plates were separated by a vacuum gap, and which was disconnected from any battery or other source of charge. We could measure the voltage difference between the plates using a voltmeter. Suppose that we inserted a slab of some insulating material (e.g., glass) into the gap between the plates, and then re-measured the voltage difference between the plates. We would find that the new voltage difference was less than , despite that fact that the charge on the plates was unchanged. Let us denote the voltage ratio as . Since, , it follows that the capacitance of the capacitor must have increased by a factor when the insulating slab was inserted between the plates.
material which has the effect of increasing the capacitance of a vacuum-filled parallel
plate capacitor, when it is inserted between its plates, is called a
dielectric material, and the factor by which the capacitance is
increased is called the dielectric constant of that material. Of course, varies from material to material. A few
sample values are given in Table 1. Note, however, that is always greater
than unity, so filling the gap between the plates of a parallel plate
capacitor with a dielectric material always increases the capacitance of the
device to some extent. On the other hand, for air is only percent greater
than for a vacuum (i.e., ), so an air-filled capacitor is virtually
indistinguishable from a vacuum-filled capacitor.
The formula for the capacitance of a dielectric-filled parallel plate capacitor
How do we explain the reduction in voltage which occurs when we insert a dielectric between the plates of a vacuum-filled parallel plate capacitor? Well, if the voltage difference between the plates is reduced then the electric field between the plates must be reduced by the same factor. In other words, the electric field generated by the charge stored on the capacitor plates must be partially canceled out by an opposing electric field generated by the dielectric itself when it is placed in an external electric field. What is the cause of this opposing field? It turns out that the opposing field is produced by the polarization of the constituent molecules of the dielectric when they are placed in an electric field (see Sect. 3.4). If is sufficiently small then the degree of polarization of each molecule is proportional to the strength of the polarizing field . It follows that the strength of the opposing field is also proportional to . In fact, the constant of proportionality is , so . The net electric field between the plates is . Hence, both the field and voltage between the plates are reduced by a factor with respect to the vacuum case. In principle, the dielectric constant of a dielectric material can be calculated from the properties of the molecules which make up the material. In practice, this calculation is too difficult to perform, except for very simple molecules. Note that the result that the degree of polarization of a polarizable molecule is proportional to the external electric field-strength breaks down if becomes too large (just as Hooke's law breaks down if we pull too hard on a spring). Fortunately, however, the field-strengths encountered in conventional laboratory experiments are not generally large enough to invalidate this result.
We have seen that when a dielectric material of dielectric
constant is placed in the uniform
electric field generated between the plates of a parallel plate capacitor then
the material polarizes, giving rise to a reduction of the field-strength
between the plates by some factor . Since there is nothing particularly
special about the electric field between the plates of a capacitor,
we surmise that this result is quite general. Thus, if space is filled
with a dielectric medium then Coulomb's law is rewritten as