FIGURE 26.29a shows a parallel-plate capacitor with the plates separated by vacuum, the perfect insulator. Suppose the capacitor is charged to voltage $(\text{Δ}{V}_{\text{C}}){}_0$, then disconnected from the battery. The charge on the plates will be $\pm Q_0$, where $Q_0=C_0(\text{Δ}{V}_{\text{C}}){}_0$. We’ll use a subscript 0 in this section to refer to a vacuum-insulated capacitor.

FIGURE 26.29 Vacuum-insulated and dielectric-filled capacitors.

Now suppose, as in FIGURE 26.29b, an insulating material, such as oil or glass or plastic, is slipped between the capacitor plates. We’ll assume for now that the insulator is of thickness d and completely fills the space. An insulator in an electric field is called a dielectric, for reasons that will soon become clear, so we call this a dielectric-filled capacitor. How does a dielectric-filled capacitor differ from the vacuum-insulated capacitor?

The charge on the capacitor plates does not change. The insulator doesn’t allow charge to move through it, and the capacitor has been disconnected from the battery, so no charge can be added to or removed from either plate. That is, $Q=Q_0$. Nonetheless, measurements of the capacitor voltage with a voltmeter would find that the voltage has decreased: $\text{Δ}{V}_{\text{C}}<(\text{Δ}{V}_{\text{C}}){}_0$. Consequently, based on the definition of capacitance, the capacitance has increased:

Example 26.6 found that the plate size needed to make a $1\mu \text{F}$ capacitor is unreasonably large. It appears that we can get more capacitance with the same plates by filling the capacitor with an insulator.

We can utilize two tools you learned in Chapter 23, superposition and polarization, to understand the properties of dielectric-filled capacitors. Figure 23.27 showed how an insulating material becomes polarized in an external electric field. FIGURE 26.30a reproduces the basic ideas from that earlier figure. The electric dipoles in Figure 26.30a could be permanent dipoles, such as water molecules, or simply induced dipoles due to a slight charge separation in the atoms. However the dipoles originate, their alignment in the electric field—the polarization of the material—produces an excess positive charge on one surface, an excess negative charge on the other. The insulator as a whole is still neutral, but the external electric field separates positive and negative charges.

FIGURE 26.30 An insulator in an external electric field.

Full Alternative Text

FIGURE 26.30b represents the polarized insulator as simply two sheets of charge with surface charge densities $\pm {\eta }_{\text{induced}}$. The size of ${\eta }_{\text{induced}}$ depends both on the strength of the electric field and on the properties of the insulator. These two sheets of charge create an electric field—a situation we analyzed in Chapter 23. In essence, the two sheets of induced charge act just like the two charged plates of a parallel-plate capacitor. The induced electric field (keep in mind that this field is due to the insulator responding to the external electric field) is

It is because an insulator in an electric field has two sheets of induced electric charge that we call it a dielectric, with the prefix di, meaning two, the same as in “diatomic” and “dipole.”