8.5 Molecular model of a dielectric  (Page 2/13)

The same effect is produced when the molecules of a dielectric are nonpolar. In this case, a nonpolar molecule acquires an induced electric-dipole moment    because the external field ${\overrightarrow{E}}_0$ causes a separation between its positive and negative charges. The induced dipoles of the nonpolar molecules align with ${\overrightarrow{E}}_0$ in the same way as the permanent dipoles of the polar molecules are aligned (shown in part (b)). Hence, the electrical field within the dielectric is weakened regardless of whether its molecules are polar or nonpolar.

Therefore, when the region between the parallel plates of a charged capacitor, such as that shown in [link] (a), is filled with a dielectric, within the dielectric there is an electrical field ${\overrightarrow{E}}_0$ due to the free charge $Q_0$ on the capacitor plates and an electrical field ${\overrightarrow{E}}_{\text{i}}$ due to the induced charge $Q_i$ on the surfaces of the dielectric. Their vector sum gives the net electrical field $\overrightarrow{E}$ within the dielectric between the capacitor plates (shown in part (b) of the figure):

This net field can be considered to be the field produced by an effective charge $Q_0-Q_i$ on the capacitor.

In most dielectrics, the net electrical field $\overrightarrow{E}$ is proportional to the field ${\overrightarrow{E}}_0$ produced by the free charge. In terms of these two electrical fields, the dielectric constant $\kappa$ of the material is defined as

Since ${\overrightarrow{E}}_0$ and ${\overrightarrow{E}}_{\text{i}}$ point in opposite directions, the magnitude E is smaller than the magnitude $E_0$ and therefore $\kappa >1.$ Combining [link] with [link] , and rearranging the terms, yields the following expression for the induced electrical field in a dielectric:

When the magnitude of an external electrical field becomes too large, the molecules of dielectric material start to become ionized. A molecule or an atom is ionized when one or more electrons are removed from it and become free electrons, no longer bound to the molecular or atomic structure. When this happens, the material can conduct, thereby allowing charge to move through the dielectric from one capacitor plate to the other. This phenomenon is called dielectric breakdown    . ( [link] shows typical random-path patterns of electrical discharge during dielectric breakdown.) The critical value, $E_{\text{c}}$ , of the electrical field at which the molecules of an insulator become ionized is called the dielectric strength    of the material. The dielectric strength imposes a limit on the voltage that can be applied for a given plate separation in a capacitor. For example, the dielectric strength of air is $E_{\text{c}}=3.0\text{MV/m}$ , so for an air-filled capacitor with a plate separation of $d=1.00\text{mm},$ the limit on the potential difference that can be safely applied across its plates without causing dielectric breakdown is $V=E_{\text{c}}d=(3.0\times {10}^6\text{V/m})(1.00\times {10}^{\mathrm{-3}}\text{m})=3.0\text{kV}$ .

However, this limit becomes 60.0 kV when the same capacitor is filled with Teflon™, whose dielectric strength is about $60.0\text{MV/m}$ . Because of this limit imposed by the dielectric strength, the amount of charge that an air-filled capacitor can store is only $Q_0={\kappa }_{\text{air}}{C}_0(3.0\text{kV)}$ and the charge stored on the same Teflon™-filled capacitor can be as much as