DK2041_01 - The rich and the poor are two locked caskets of...

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Unformatted text preview: The rich and the poor are two locked caskets of which each contains the key to the other. Karen Blixen (Danish Writer) 1 INTRODUCTORY CONCEPTS I n this Chapter we recapitulate some basic concepts that are used in several chapters that follow. Theorems on electrostatics are included as an introduction to the study of the influence of electric fields on dielectric materials. The solution of Laplace's equation to find the electric field within and without dielectric combinations yield expressions which help to develop the various dielectric theories discussed in subsequent chapters. The band theory of solids is discussed briefly to assist in understanding the electronic structure of dielectrics and a fundamental knowledge of this topic is essential to understand the conduction and breakdown in dielectrics. The energy distribution of charged particles is one of the most basic aspects that are required for a proper understanding of structure of the condensed phase and electrical discharges in gases. Certain theorems are merely mentioned without a rigorous proof and the student should consult a book on electrostatics to supplement the reading. 1.1 A DIPOLE A pair of equal and opposite charges situated close enough compared with the distance to an observer is called an electric dipole. The quantity » = Qd (1.1) where d is the distance between the two charges is called the electric dipole moment, u. is a vector quantity the direction of which is taken from the negative to the positive • j r . charge and has the unit of C m. A unit of dipole moment is 1 Debye = 3.33 xlO" C m. 1.2 THE POTENTIAL DUE TO A DIPOLE Let two point charges of equal magnitude and opposite polarity, +Q and -Q be situated d meters apart. It is required to calculate the electric potential at point P, which is situated at a distance of R from the midpoint of the axis of the dipole. Let R + and R . be the distance of the point from the positive and negative charge respectively (fig. 1.1). Let R make an angle 6 with the axis of the dipole. R Fig. 1.1 Potential at a far away point P due to a dipole. The potential at P is equal to Q R_ (1.2) Starting from this equation the potential due to the dipole is , QdcosQ (1.3) Three other forms of equation (1.3) are often useful. They are (1.4) (1.5) (1.6) The potential due to a dipole decreases more rapidly than that due to a single charge as the distance is increased. Hence equation (1.3) should not be used when R « d. To determine its accuracy relative to eq. (1.2) consider a point along the axis of the dipole at a distance of R=d from the positive charge. Since 6 = 0 in this case, (f> = Qd/4ns (1.5d) =Q/9ns d according to (1.3). If we use equation (1.2) instead, the potential is Q/8ns d, an error of about 12%....
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DK2041_01 - The rich and the poor are two locked caskets of...

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