Experiments indicate that all dielectric materials have e 1 Note that every

Experiments indicate that all dielectric materials

This preview shows page 47 - 49 out of 110 pages.

their dielectric constant. Experiments indicate that all dielectric materials have e 1. Note that every dielectric material has a characteristic dielectric strength which is the maximum value of electric field before breakdown occurs and charges begin to flow. Material e Dielectric strength 10 6 V / m Air 1.00059 3 Paper 3.7 16 Glass 4 6 9 Water 80 The fact that capacitance increases in the presence of a dielectric can be explained from a molecular point of view. We shall show that e is a measure of the dielectric response to an external electric field. There are two types of dielectrics. The first type is polar dielectrics, which are dielectrics that have permanent electric dipole moments. An example of this type of dielectric is water. . Figure 4.5.1 Orientations of polar molecules when (a) E 0 0 and (b) E 0 0 . As depicted in Figure 4.5.1, the orientation of polar m . olecules is random in the absence of an external field. When an external electric field E 0 is present, a torque is set up and causes the molecules to align with E 0 . However, the alignment is not complete due to random thermal motion. The aligned molecules then generate an electric field that is opposite to the applied field but smaller in magnitude. The second type of dielectrics is the non-polar dielectrics, which are dielectrics that do not possess permanent electric dipole moment. Electric dipole moments can be induced by placing the materials in an externally applied electric field.
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48 Figure 4.5.2 Orientations of non-polar molecules when (a) ? 0 = 0 and (b) ? 0 ≠ 0 Figure 4.5.2 illustrates the orientation of non-polar molecules with and without an external field ? 0 . The induced surface charges on the faces produces an electric field ? ? in the direction opposite to ? 0 , leading to ? = ? 0 + ? 0 , with |? | < ? 0 . Below we show how the induced electric field E P is calculated. 4.5.1. Polarization We have shown that dielectric materials consist of many permanent or induced electric dipoles. One of the concepts crucial to the understanding of dielectric materials is the average electric field produced by many little electric dipoles which are all aligned. Suppose we have a piece of material in the form of a cylinder with area A and height h , as shown in Figure 4.5.3, and that it consists of N electric dipoles, each with electric dipole moment ? spread uniformly throughout the volume of the cylinder. Figure 4.5.3 A cylinder with uniform dipole distribution. We furthermore assume for the moment that all of the electric dipole moments ? are aligned with the axis of the cylinder. Since each electric dipole has its own electric field associated with it, in the absence of any external electric field, if we average over all the individual fields produced by the dipole, what is the average electric field just due to the presence of the aligned dipoles?
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