Physics
Electric Dipole
An electric dipole is a pair of equal and opposite electric charges separated by a small distance. It is characterized by a dipole moment, which is the product of the charge magnitude and the separation distance. Electric dipoles are important in understanding the behavior of electric fields and are commonly used in various applications, such as antennas and molecular interactions.
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12 Key excerpts on "Electric Dipole"
eBook - PDFTheory of Electric Polarization
Dielectrics in Static Fields
- Bozzano G Luisa(Author)
- 2012(Publication Date)
- Elsevier Science(Publisher)
We then have: m = le. (1.2) Therefore, the electric moment of a system of charges with zero net charge is generally called the Electric Dipole moment of the system. A simple case is a system consisting of only two point charges +e and — e at a distance I. Such a system is called a (physical) Electric Dipole, its moment is equal to el, the vector / pointing from the negative to the positive charge. In theoretical organic chemistry the dipole vector is generally taken as pointing from the positive to the negative charge. We prefer to use the physical definition given above. A mathematical abstraction derived from the above defined physical dipole is the ideal or point dipole. Its definition is as follows: the distance / between two point charges + e and — e is replaced by l/n and the charge e by en. The limit approached as the number η tends to infinity is the ideal dipole. The equations derived for ideal dipoles are much simpler than those obtained for non-ideal dipoles. Many neutral molecules are examples of charge systems with a non-ideal Electric Dipole moment, since in most types of molecule the centres of gravity of the positive and negative charge distributions do not coincide. Apart from these permanent or intrinsic dipole moments, a temporary or induced dipole moment arises when a particle is brought into an external electric field. Under the influence of this field the positive and negative charges in the particle are moved apart: the particle is polarized. In general, these induced dipoles can be treated as ideal; permanent dipoles, however, may generally not be treated as ideal when the field at molecular distances is to be calculated (see section 2). Electric DipoleS AND MULTIPOLES 11 The values of molecular dipole moments are usually expressed in Debye units. The Debye unit, abbreviated as D, equals 1 0 1 8 electrostatic units (e.s.u.). The permanent dipole moments of non-symmetrical molecules generally lie between 0.5 and 5D.
- Jian-Ming Jin(Author)
- 2015(Publication Date)
- Wiley-IEEE Press(Publisher)
As a result, in both atoms and nonpolar molecules, the effective center of positive charges will be displaced from the effective center of negative charges, creating a tiny Electric Dipole in the direction of the electric field. (Here, we assume that the applied field is not strong enough to break the bound electrons loose from the nuclei. In such a case, the matter is often called a dielectric .) In the case of polar molecules, because of the Lorentz force, all the randomly oriented dipoles tend to line up with the applied electric field. When a large number of Electric Dipoles line in the same direction, the electric fields created by the dipoles add up and these electric fields are in the opposite direction to the applied field, resulting in a weaker total electric field in the medium. To quantify the effect of tiny dipoles, a vector quantity called the dipole moment is defined as 𝓅 = q 𝓁 (1.3.1) where q denotes the charge and 𝓁 denotes the vector pointing from the effective center of the negative charge to that of the positive charge. The sum of dipole moments per unit volume is then P = lim Δ 𝑣 → 0 1 Δ 𝑣 n p i = 1 𝓅 i (1.3.2) where n p denotes the number of dipoles contained in Δ 𝑣 . The dipole moment density P is also called the polarization intensity or polarization vector . When the dipole moment density is uniform, the positive charge of a dipole is completely canceled by the negative charge of the next dipole; hence, there is no net charge in the medium. However, when the dipole moment density is not uniform, the positive charge of 20 BASIC ELECTROMAGNETIC THEORY a dipole cannot be completely canceled by the negative charge of the next dipole, resulting in a net charge at the point and hence a volume charge density. Based on the definition of divergence, this volume charge density is given by 𝜚 e , b = −∇ ⋅ P (1.3.3) where the subscript “b” is used to denote that this is the density of the bound charges.
eBook - PDF- M. Sibley(Author)
- 1995(Publication Date)
- Butterworth-Heinemann(Publisher)
The dipole momentis a vector quantity with direction towardsthe positive charge. The reasonfor this choice ofdirection will becomeclearin the next section. In most materials,the separationbetweenthechargesis directly dependent on the magnitudeof the external E field. However,if we continuallyincrease the E field, therecomes apointwherewe cannotpolarizethe atomany more. 8 Dielectrics In. this chapte r we will re-examine capacitor s and, in particular , the effect of an electric field on dielectrics , As we saw in Chapte r 2» dielectrics have a permittivity greate r than air. Thus, when we use them as the insulating materia l in a capacitor , they increase the capacitance « If the potentia l across the plates is constant , the stored charge will increase and so it is generall y desirabl e to design a capacito r with a dielectric, The next section introduces the dipole momen t that occurs when an electric field distorts an atom, or molecule . 6,1 ELECTRIC DSPOLES AND DIPOLE MOMENTS If we have an. atom thai is well away from any externa l electric field, the orbit of the electrons will describe a spher e with the nucleus at the centre (see Fig. 6.1(a)). If we place this atom in an electric field, the field will distort the atom as Fig, 6.1(b) shows , In effect, the electron cloud moves away from the field» whereas the positiYely charged nucleus moYes in the direction of the field. The atom is said to be polarized by the electric field. Although the polarized atom is still electricall y neutral , on the microscopi c scal e the atom has an electric field, This becomes cleare r if we replace the electron cloud by a point source at a distance d from the positive nucleus .
eBook - ePub- Albert Shadowitz(Author)
- 2012(Publication Date)
- Dover Publications(Publisher)
Here one charge must be the negative of the other. Such a distribution of two charges, one the negative of the other, is called an Electric Dipole. Note the different, distinct, ways in which the term dipole is used here. (1) The dipole term is the r -2 term in the multipole expansion of an arbitrary charge distribution. (2) The dipole moment is the magnitude of a vector, of which the numerator of the dipole term is the longitudinal component. (3) The Electric Dipole is a specific distribution of two charges, equal but opposite, placed at two different points; it is implicit that the separation between the charges is much smaller than the distance to the field point. The potential ϕ ∝ r -2 produced at distant points by a dipole falls off much more rapidly with increasing distance than that produced by a single point charge ϕ ∝ r -1. That of the dipole is the residue remaining when two equal but opposite charges almost, but not quite, cancel each other. The name dipole stems from the fact that two opposite charges are required for an invariant dipole moment. The dipole distribution is an extremely important one because it provides the key to the explanation of the problems raised by the behavior of matter in the presence of an electric field. The remainder of this chapter is essentially devoted to the further exploration of this subject. If the dipole moment is zero then the quadrupole term becomes the leading term in the expansion of the potential. This term falls off with distance much more rapidly than the term preceding it, the dipole term. At a point far from the charges it is the remainder that is left when two equal but opposite dipoles almost, but not exactly, cancel each other. The name “quadrupole” comes from 2 n = 4 with n = 2. Two pairs of equal and opposite charges are required to have both the total charge and the dipole moment vanish. This requires four charges, therefore. Figure 6-2 a shows a simple dipole charge distribution
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
. . 22.10 Draw an Electric Dipole, identifying the charges (sizes and signs), dipole axis, and direction of the Electric Dipole moment. 22.11 Identify the direction of the electric field at any given point along the dipole axis, including between the charges. 22.12 Outline how the equation for the electric field due to an Electric Dipole is derived from the equa- tions for the electric field due to the individual charged particles that form the dipole. 22.13 For a single charged particle and an Electric Dipole, compare the rate at which the electric field magnitude decreases with increase in distance. That is, identify which drops off faster. 22.14 For an Electric Dipole, apply the relationship between the magnitude p of the dipole moment, the separation d between the charges, and the magnitude q of either of the charges. 22.15 For any distant point along a dipole axis, apply the relationship between the electric field magnitude E, the distance z from the center of the dipole, and either the dipole moment magnitude p or the product of charge magnitude q and charge separation d. Key Ideas ● An Electric Dipole consists of two particles with charges of equal magnitude q but opposite signs, separated by a small distance d. ● The Electric Dipole moment p → has magnitude qd and points from the negative charge to the positive charge. ● The magnitude of the electric field set up by an Electric Dipole at a distant point on the dipole axis (which runs through both particles) can be written in terms of either the product qd or the magnitude p of the dipole moment: E = 1 2πε 0 qd z 3 = 1 2πε 0 p z 3 , where z is the distance between the point and the center of the dipole. ● Because of the 1/z 3 dependence, the field magnitude of an Electric Dipole decreases more rapidly with dis- tance than the field magnitude of either of the individual charges forming the dipole, which depends on 1/r 2 .
eBook - ePub- Sivaji Chakravorti(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
On the other hand, there are large numbers of dielectric materials containing molecules having permanent dipole moment. In those cases, the permanent dipoles will be aligned by the external electric field in its direction. The degree of alignment of permanent dipoles is higher for stronger external field. The net dipole moment of a dielectric piece is typically zero, when not influenced by external electric field, because the atoms have zero dipole moment and the permanent dipoles are randomly oriented. But due to the induction or alignment of dipoles under the action of external electric field, a dielectric piece may be considered as arrays of oriented Electric Dipoles. As a result, a dielectric piece acquires a net dipole moment and the dielectric is said to be polarized. The process by which a dielectric material gets polarized is known as polarization. 5.2 Field due to an Electric Dipole and Polarization Vector A polarized dielectric can be assumed to be a collection of oriented Electric Dipoles situated in vacuum. If the charges of the Electric Dipoles and the distances between them are known, then it is possible to determine the electric potential and electric field intensity at any external location due to the polarized dielectric. But this is practically very difficult due to immensely large number of such dipoles in a polarized dielectric. Because of this reason, a kind of average dipole density is defined in the form of a vector quantity known as polarization vector for the ease of analysis. 5.2.1 Electric Dipole and Dipole Moment When two point charges of equal magnitude but of opposite polarities are separated by a small distance, then the arrangement is known as an Electric Dipole, as shown in Figure 5.1. For field analysis, it is required that a single dipole be characterized by a vector quantity. As depicted in Figure 5.1, let the magnitudes of the charges be + Q and − Q, respectively, and the distance between them is d
eBook - PDF- Pierluigi Zotto, Sergio Lo Russo, Paolo Sartori(Authors)
- 2022(Publication Date)
- Società Editrice Esculapio(Publisher)
Unfortunately, the magnitude of the elec- tric dipole moment of a molecule differs from the Electric Dipole moment of any other one, so statistical methods must be applied in order to perform a sensible quantitative descrip- tion of the phenomenon. Hence, an amount of material sufficiently small to be assumed as an elementary volume dV of material, but at the same time being composed by a number of molecules dN sufficiently large to assume the validity of the use of average values, must be considered. In such a case the overall Electric Dipole moment of the material, obtained by the vector sum of the Electric Dipole moment p i of each molecule, can be expressed as d p = p i i =1 N ∑ = dN p 0 = n p 0 dV , E 0 +q –q V + V – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – E p Dielectrics Chapter 6 82 where p 0 is the average Electric Dipole moment of a molecule along the direction of the polarising field E 0 and n = dN dV is the number of aligned dipoles per unit volume. Hence, the vector P = d p dV = n p 0 represents the Electric Dipole moment per unit of volume of the material and it is called electric polarisation density. Missing a polarising field E 0 , the average dipole moment is p 0 = 0, also in the case of polar molecules due to the random distribution of the Electric Dipole moment of each mole- cules caused by thermal agitation, and therefore the material is not polarised. If a polarising field E 0 ≠ 0 exists, also an average Electric Dipole p 0 ≠ 0 exists and it is oriented along the direction of the polarising electric field. As a consequence, an electric polarisation density P parallel and concordant to field E 0 appears. The simplest case is the appearance of a uniform electric polarisation, which corre- sponds to the case where the polarising field is uniform and constant.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
3. The magnitude of the electric field set up by an Electric Dipole at a distant point on the dipole axis (which runs through both particles) can be written in terms of either the product qd or the magnitude p of the dipole moment: E = 1 _____ 2πε 0 qd ___ z 3 = 1 _____ 2πε 0 p ___ z 3 , where z is the distance between the point and the center of the dipole. 4. Because of the 1/z 3 dependence, the field magnitude of an Electric Dipole decreases more rapidly with distance than the field magnitude of either of the individual charges forming the dipole, which depends on 1/r 2 . LEARNING OBJECTIVES The Electric Field Due to an Electric Dipole Figure 22.3.1 shows the pattern of electric field lines for two particles that have the same charge magnitude q but opposite signs, a very common and important 22.3 The Electric Field Due to a Dipole 635 arrangement known as an Electric Dipole. The particles are separated by distance d and lie along the dipole axis, an axis of symmetry around which you can imagine rotating the pattern in Fig. 22.3.1. Let’s label that axis as a z axis. Here we restrict our interest to the magnitude and direction of the electric field E → at an arbitrary point P along the dipole axis, at distance z from the dipole’s midpoint. Figure 22.3.2a shows the electric fields set up at P by each particle. The nearer particle with charge +q sets up field E (+) in the positive direction of the z axis (directly away from the particle). The farther particle with charge −q sets up a smaller field E (−) in the negative direction (directly toward the particle). We want the net field at P, as given by Eq. 22.2.3. However, because the field vectors are along the same axis, let’s simply indicate the vector directions with plus and minus signs, as we commonly do with forces along a single axis.
eBook - PDF- Edward Purcell(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
We are interested only in the electric field they produce when they are in this condition; later we can introduce any fields from other 365 Water ! p = 1.84 Methanol /? p = 1.70 FIGURE 10.14 Some well-known polar molecules. The observed magnitude 01 tile permanent dipole moment p is g iven in units of 10- 18 esu-cm. 366 z Area da P 1 0 L· /-' r- dt. (a) Charge + Pda Charge -Pda (b) FIGURE 10.15 x A column of polarized material (a) produces the same field, at any external point A, as two charges, one at each end of the column (b). CHAPTER TEN sources that might be around. If you like, you can imagine that these are molecules with permanent dipole moments that have been lined up neatly, all pointing the same way, and frozen in position. All we need to specify is N, the number of dipoles per cubic centimeter, and the moment of each dipole p. We shall assume that N is so large that any macroscopically small volume du contains quite a large number of dipoles. The total dipole strength in such a volume is pN du. At any point far away from this volume element compared with its size, the electric field from these particular dipoles would be practically the same if they were replaced by a single dipole moment of strength pN du. We shall call pN the density of polarization, and denote it by P, a vector quantity with the dimensions charge-cm/cm 3 , or charge per cm 2 • Then P du is the dipole moment to be associated with any small- volume element du for the purpose of computing the electric field at a distance. By the way, our matter has been assembled from neutral molecules only; there is no net charge in the system or on any mole- cule, so we have only the dipole moments to consider as sources of a distant field. In Fig. 10.15 there is shown a slender column, or cylinder, of this polarized material. Its cross section is da, and it extends vertically from ZI to Z2. The polarization density P within the column is uniform over the length and points in the positive Z direction.
eBook - ePubDielectrophoresis
Theory, Methodology and Biological Applications
- Ronald R. Pethig(Author)
- 2017(Publication Date)
- Wiley(Publisher)
3 Electric Charges, Fields, Fluxes and Induced Polarization3.1 Introduction
A dielectric can be defined as a material that is a poor conductor of electricity and is capable of supporting an electrostatic field. Other definitions that are given sometimes also include words to the effect that a dielectric becomes polarized when exposed to an electric field. Thus, introductions to the theoretical concepts of dielectric phenomena [e.g., 1] often commence with the scheme shown in Figure 2.1 of Chapter 2, where a voltage potential difference is applied across two parallel metal plates located in a vacuum. The applied potential difference generates a distribution of equal and opposite free electrical charges on the faces of the plates (denoted by symbols +, − in Figure 2.1). The next step is to remove the external voltage source and to replace it with a voltage measuring device, such as an electrometer. The only factor that controls the voltage across the metal plates is the density of free charge on the surfaces of the plates. To ensure that this voltage remains constant and is not affected by the measurement of it, a voltmeter is designed to have a very high resistance to electric current flow. We can therefore ignore any leakage of charge through the electrometer that might reduce the density of positive and negative free charges on the plates. The voltage potential difference across the plates with vacuum between them is measured as V0 . The exercise is then performed of inserting a solid slab of dielectric material into the space between the plates, whilst noting the reading on the electrometer. It is found, as depicted in Figure 3.1 , that the voltage reading falls to a new value V1 . The distance d between the plates remains fixed, so we can assume that the electric field (V/d) between the plates has also dropped from E0 to E1 . The ratio E0 /E1 (or V0 /V1 ) is defined as the relative permittivity r
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The electric field vector at any point is tangent to a field line through that point. The density of field lines in any region is proportional to the magnitude of the electric field in that region. Field lines originate on positive charges and terminate on negative charges. Field Due to a Point Charge The magnitude of the elec- tric field E → set up by a point charge q at a distance r from the charge is E = 1 _____ 4πε 0 |q| ___ r 2 . (22.2.2) The direction of E → is away from the point charge if the charge is positive and toward it if the charge is negative. Field Due to an Electric Dipole An Electric Dipole con- sists of two particles with charges of equal magnitude q but opposite sign, separated by a small distance d. Their elec- tric dipole moment p → has magnitude qd and points from the negative charge to the positive charge. The magnitude of the electric field set up by the dipole at a distant point on the dipole axis (which runs through both charges) is E = 1 _____ 2πε 0 p _____ z 3 , (22.3.5) where z is the distance between the point and the center of the dipole. Review & Summary Field Due to a Continuous Charge Distribution The electric field due to a continuous charge distribution is found by treating charge elements as point charges and then summing, via integration, the electric field vectors produced by all the charge elements to find the net vector. Field Due to a Charged Disk The electric field magni- tude at a point on the central axis through a uniformly charged disk is given by E = σ ____ 2 ε 0 ( 1 − z _________ √ _ z 2 + R 2 ) , (22.5.5) where z is the distance along the axis from the center of the disk, R is the radius of the disk, and σ is the surface charge density. Force on a Point Charge in an Electric Field When a point charge q is placed in an external electric field E → , the elec- trostatic force F → that acts on the point charge is F → = qE → .
eBook - ePubSome Electrical and Optical Aspects of Molecular Behaviour
The Commonwealth and International Library: Chemistry Division
- Mansel Davies, Robert Robinson, H. M. N. H. Irving, L. A. K. Staveley(Authors)
- 2014(Publication Date)
- Pergamon(Publisher)
* But it is clear that the simpler electrostatic features predominate in many systems and that on their basis one obtains an approximate assessment of the interactions occurring. As it is the energy factor which determines the functional importance of most interactions, it is frequently necessary to see what contributions arise from electrostatic factors before invoking other possibilities.Using electrostatic (c.g.s.) units we can write down the expressions for the forces F (in dyne) or the energies U (in erg molecule−1 ) for various particle interactions. As we have already seen (p. 11 ), -ΔU = F . Δr , where -ΔU is the decrease in energy when a particle moves a distance Δr under force F. This gives the general expression, F = -(dU/ dr) and we can conveniently restrict ourselves to the expressions for U.Ion-Ion
Two ions behaving as rigid electric chargeszA eandzB e,where z is the number of electronic charges e involved, have energy:where r is their separation and the z ’s take account of their sign (+ or -) and ε′ is the permittivity of any medium between them. The energy is positive for the like charges and increases as r decreases. The instability expressed by the increasing energy is reflected by the repulsion or negative F values: conditions which are reversed for unlike charges.Ion-Dipole
A dipole μ at angle θ to a field E (Fig. 11 ) has energy μμE cos θ. If an ion, charge ze, is at distance r from the centre of the dipole the field is . In this caseTwo Rigid Dipoles
With the orientation and dimensions shown in Fig. 60 , and with rlA≈lB= l , so that etc.FIG. 60If one of the dipoles rotates through 180° with respect to the other, the above sign is reversed and U (r ) then expresses the net repulsion. Lateral alignment with dipole centres still at distance r (Fig. 60(b)
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