Physics · Ch 10 — Electrostatics

Electric Dipole

10.9

Electric Dipole

A pair of equal and opposite point charges, $+q$ and $-q$ , separated by some finite distance, is called an ELECTRIC DIPOLE (Fig. 10.18). The straight line joining the two charges is called the DIPOLE AXIS; any line lying along (passing through) the dipole axis is called an AXIAL LINE; and the line passing through the exact centre (midpoint) of the dipole, perpendicular to the axial line, is called the EQUATORIAL LINE.

The overall 'strength' of a dipole is measured by a single quantity called the DIPOLE MOMENT. If q is the magnitude of each of the two charges, and $2l$ is the distance separating the negative charge from the positive charge, the dipole moment is defined as the product $\vec{p}=q(2\vec{l}).$ Dipole moment is a VECTOR quantity: its magnitude is $q(2l)$ , and its direction is defined to run FROM the negative charge TOWARD the positive charge. The SI unit of dipole moment is the coulomb-metre (C m); a smaller, more practical unit commonly used at the molecular scale is the DEBYE (D), where $1\,D=3.33\times10^{-30}$ C m. As a sense of scale, if charges of $+e$ and $-e$ were separated by a distance of just $1.0\,\text{\AA}=10^{-10}$ m (a typical atomic-scale separation), the resulting dipole moment would be about $1.6\times10^{-29}$ C m, or 4.8 D. …

Figure 10.18Fig. 10.18: An electric dipole, showing its axial and equatorial lines

What this figure shows. Two point charges, $-q$ at one end (marked x) and $+q$ at the other end (marked y), separated by a distance $2l$ , joined by a straight line -- the dipole axis. This axis, extended in both directions, is labelled the AXIAL LINE (x-y). A second line, labelled P-Q, is drawn passing through the exact midpoint (centre) of the dipole axis, at right angles to it -- this is the EQUATORIAL LINE. The figure establishes the basic geometric vocabulary (dipole axis, axial line, equatorial line, and the separation $2l$ between the two equal-and-opposite charges) used throughout the rest of the section for computing to …

Misc DYK.4Do you know? -- Natural (permanent) dipoles: polar and non-polar molecules

Worked out. A water molecule is non-linear -- its two O-H bonds meet at an angle of $105^\circ$ -- so its positive charge (concentrated on the hydrogen side) and negative charge (concentrated on the oxygen side) are inherently separated by a small distance, giving water a PERMANENT dipole moment of about $6.172\times10^{-30}$ C m (1.85 D), directed from oxygen to hydrogen. Molecules like water, ammonia, sulphur dioxide and sodium chloride, whose positive and negative charge centres are naturally offset, are called POLAR molecules. Molecules such as $H_2$ , $Cl_2$ , $CO_2$ and $CH_4$ , whose positive and negative charge centres coincide exactly at the same point, are called NON-POLAR molecules and have no permanent dipole moment -- though an external electric field can still displace their cha …

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