Physics
Electric Dipole Radiation
Electric dipole radiation refers to the electromagnetic radiation emitted by an oscillating electric dipole. When an electric dipole undergoes acceleration, it generates changing electric and magnetic fields, resulting in the emission of electromagnetic waves. This radiation pattern is characterized by a non-uniform distribution of energy, with the strongest radiation occurring perpendicular to the dipole axis.
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11 Key excerpts on "Electric Dipole Radiation"
- Zeev Burshtein(Author)
- 2022(Publication Date)
- Wiley(Publisher)
The units of the electric dipole moment are charge times length units; in the cgs system they are esu cm, or alternatively (erg cm 3 ) 1/2 . 1 Physics, Optics, and Spectroscopy of Materials, First Edition. Zeev Burshtein. © 2022 John Wiley & Sons, Inc. Published 2022 by John Wiley & Sons, Inc. We consider the radiation emitted by an electric dipole Q z , vibrating harmonically at an ω 0 angular frequency Q z t = Q 0 cos ω 0 t 1 1 For simplicity, we begin by assuming that the maximal dipole strength Q 0 is a time-independent constant. We will show that this assumption requires correction to be quantitatively assessed. The issue of radiation emitted by the dipole has been classically solved. In free space, at a distance r which is large compared to the wavelength λ (λ = 2πc/ω 0 , where c is the vacuum speed-of-light constant), the electric and magnetic fields are given by E = H = 1 c 2 r Q z t - r c sin θ 1 2 The electric field E and magnetic field H vectors are mutually perpendicular (see Figure 1.1), and θ is the angle between the Z-axis direction and the r vector direction. Both are perpendicular to r . The situation addressed in the figure is for the part of the vibrational period where the magnetic field H points into the page. When the magnetic field H points outward, the electric field E reverses orientation as well. The phase common to both E and H lags behind the vibrating dipole phase according to the radiation propagation time-delay r/c. Notably, the vibrating fields amplitudes diminish when the r vector direction coincides with the Z-axis direction (θ = 0), and attain maximal value when r is perpendicular to Z. An equation identical to Eq. (1.2) will be obtained for any r orientation if the dipole in Figure 1.1 is exchanged by its projection on a plane perpendicular to r . The radiation is linearly polarized in the ( r , Q) plane. Eq. (1.2) describes an electromagnetic radiation propagating away from the vibrating dipole.
eBook - PDF- David J. Griffiths(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
466 11.1 Dipole Radiation 467 (with t 0 held constant). This is energy (per unit time) that is carried away and never comes back. Now, the area of the sphere is 4π r 2 , so for radiation to occur the Poynting vec- tor must decrease (at large r ) no faster than 1/r 2 (if it went like 1/r 3 , for example, then P would go like 1/r , and P rad would be zero). According to Coulomb’s law, electrostatic fields fall off like 1/r 2 (or even faster, if the total charge is zero), and the Biot-Savart law says that magnetostatic fields go like 1/r 2 (or faster), which means that S ∼ 1/r 4 , for static configurations. So static sources do not radiate. But Jefimenko’s equations (Eqs. 10.36 and 10.38) indicate that time-dependent fields include terms (involving ˙ ρ and ˙ J) that go like 1/r ; these are the terms that are responsible for electromagnetic radiation. The study of radiation, then, involves picking out the parts of E and B that go like 1/r at large distances from the source, constructing from them the 1/r 2 term in S, integrating over a large spherical 4 surface, and taking the limit as r → ∞. I’ll carry through this procedure first for oscillating electric and magnetic dipoles; then, in Sect. 11.2, we’ll consider the more difficult case of radiation from an accelerating point charge. 11.1.2 Electric Dipole Radiation Picture two tiny metal spheres separated by a distance d and connected by a fine wire (Fig. 11.2); at time t the charge on the upper sphere is q (t ), and the charge on the lower sphere is −q (t ). Suppose that we drive the charge back and forth through the wire, from one end to the other, at an angular frequency ω: q (t ) = q 0 cos(ωt ). (11.3) The result is an oscillating electric dipole: 5 p(t ) = p 0 cos(ωt ) ˆ z, (11.4) where p 0 ≡ q 0 d is the maximum value of the dipole moment.
eBook - PDF- Tung Tsang(Author)
- 1998(Publication Date)
- WSPC(Publisher)
CHAPTER 7 RADIATING SYSTEMS 7.1 Electric Dipole Radiation In radiation and antenna systems, we are interested in finding the electromagnetic (EM) fields in the presence of localized oscillating systems of current density J and charge density pe: J(r,t)=a(r)c-tot Pe(r,t)=p e (r)e-i t » t (7.1) where r and t are position vector and time, co (in radians/sec) is the frequency of the oscillation. We will consider the radiation process in vacuum where e=ji=l. To introduce the current density J, it is convenient to start from the vector potential A in the Lorentz gauge (Sec. 4.6): ~ 1 a 2 A 4« -V 2 A + — — - = — J c at c ( 7 2 ) B=VxA (7.3) where eqs. (4.48) and (4.41) have been re-numbered as eqs. (7.2) and (7.3). We will use the primed notation (r',f) for the source. We will use the unprimed notation (r,t) for the field point where the observer is located and measurements of the EM fields of the radiation are performed. J and p e are limited to the interior of a small source region as shown in Fig. 7.1.The origin O of our coordinate system is inside the source region. The vector potential A and the magnetic field B refers to the field point r. We can calculate the electric field E at the field point from the modified Ampere law (eq. 4.10c). Since J=0 at the field point, we get: 4jt w H E i a E i
eBook - PDF- Hector Perez-de-Tejada(Author)
- 2017(Publication Date)
- IntechOpen(Publisher)
The figure shows the flow lines of energy for a dipole midway between the mirrors, and oscillating under 45° with the z -axis. Figure 19. The figure shows the flow lines of energy for a horizontal dipole midway between the mirrors. Figure 21. The figure shows the flow lines of energy for a dipole close to the lower mirror and oscillating horizontally. Vortices and Singularities in Electric Dipole Radiation near an Interface http://dx.doi.org/10.5772/66459 313 dipole, but it is now closer to the mirror on the bottom. Numerous vortices appear in the flow pattern. 10. Conclusions An oscillating electric dipole in free space emits its energy along straight lines. Most radiation is emitted perpendicular to the dipole axis, and none comes out along the dipole axis. We have studied the effect of a nearby interface on this flow pattern. Reflection of radiation at the interface leads to interference between the directly emitted radiation and the reflected radia-tion. A mirror is impenetrable for radiation, and so all radiation bounces back at the interface. This also implies that the field lines of energy flow must be parallel to the mirror at the mirror surface. This effect is shown in Figure 3 for a dipole oscillating perpendicular to the surface, and one wavelength away from the surface. The radiation comes out of the dipole, more or less as for emission in free space, but at the mirror surface the field lines bend, and the energy flows away along the mirror surface. For a dipole oscillating parallel to the surface, a typical flow pattern is shown in Figure 4 . Again, at the mirror surface the field lines run away parallel to the surface, but in between the surface and the dipole several singularities appear, and there is also a vortex very close to the dipole. For the case shown in Figure 5 , the dipole oscillates under 45° with the normal to the surface, and we see that two large vortices appear and one very small one.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
• is the distance from the doublet to the point where the electrical field is evaluated. • is the wavenumber The exponent of accounts for the phase dependence of the electrical field on time and the distance from the dipole. The far electric field of the electromagnetic wave is coplanar with the conductor and perpendicular with the line joining the dipole to the point where the field is evaluated. If the dipole is placed in the center of a sphere in the axis south-north, the electric field would be parallel to geographic meridians and the magnetic field of the electromagnetic wave would be parallel to geographic parallels. Near Field The above formulas are valid for the far field of the antenna ( ), and are the only contribution to the radiated field. The formulas in the near field have additional terms that reduce with r 2 and r 3 . These are, ________________________ WORLD TECHNOLOGIES ________________________ where . The energy associated with the term of the near field flows back and forward out and into the antenna. Short dipole A short dipole is a physically feasible dipole formed by two conductors with a total length very small compared with the wavelength . The two conducting wires are fed at the centre of the dipole. We assume the hypothesis that the current is maximal at the centre (where the dipole is fed) and that it decreases linearly to be zero at the ends of the wires. Note that the direction of the current is the same in both the dipole branches - to the right in both or to the left in both. The far field of the electromagnetic wave radiated by this dipole is: ________________________ WORLD TECHNOLOGIES ________________________ Emission is maximal in the plane perpendicular to the dipole and zero in the direction of wires which is the direction of the current. The emission diagram is circular section torus shaped (right image) with zero inner diameter. In the left image the doublet is vertical in the torus centre.
eBook - PDF- Tapan K. Sarkar, Magdalena Salazar Palma, Mohammad Najib Abdallah(Authors)
- 2018(Publication Date)
- Wiley-IEEE Press(Publisher)
However, the radiation pattern is omni‐direc-tional along a horizontal plane. In any case, the far field pattern is not pertinent for a wireless system since a mobile user will invariably be in the near field for all practical purposes under current deployment situations over a high tower. Hence, one needs to carefully look at the near field of this antenna, which can be computed accurately using the Maxwell’s equations and taking into account the effects of the environment [7, 20, 21] and will be discussed in details in Chapter 3. For the sake of completeness, we consider the same half wave dipole antenna now placed on top of the tower but situated over a real Earth which is 1.4 (a) (b) 0.0 0.0 90.0 abs( rE uni03B8 ) [V] abs( rE uni03B8 ) [V] 1.4 0.0 70.0 90.0 uni03B8 uni03B8 Figure 2.17 Radiation pattern of a dipole (a) normal, and (b) expended, situated on top of a 20 m tower located over a perfectly conducting ground. 2 Characterization of Radiating Elements Using Electromagnetic Principles 98 considered to be an imperfectly conducting ground. Thereby, we can charac-terize the real Earth, let us say, by sandy soil, for an assumed relative permittiv-ity of ε r = 10, and a conductivity of σ = 2×10 −3 mhos/m [2, p. 893]. The radiation pattern for this elevated dipole is shown in Figure 2.18. (The field pattern is calculated using the commercial software package AWAS [7], which uses the Sommerfeld formulation as explained in Chapter 3). Observe that near the ground, the pattern is dramatically different from the perfectly conducting case. The plots are similar to Figure 2.15, except that the fields are zero along the Earth in contrast to the perfectly ground case. This is due to the losses in the earth and the fields at infinity becomes zero. But near the zenith the field plots are different as the strength of the field from the image is weaker due to the assumption of an imperfectly conducting ground.
- Heinrich F. Beyer, Viateheslav P. Shevelko(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
The terms light, radiation, rays and waves characterize the same phenomenon and are often used as synonyms. Electromagnetic waves, i.e. periodically fluctuating electric and magnetic fields are matterless patterns, series of events that happen repeatedly. Physically they are described by transverse waves periodic in time and space and are characterized by the wavevector k , their period T , wavelength λ and the amplitudes E 0 of the electric field and B 0 of the magnetic field, respectively. An 21 22 Radiation Figure 2.1. A linearly polarized electromagnetic plane wave. example of a linearly polarized electromagnetic wave is illustrated in figure 2.1. The wavelength is the distance between two successive wave crests which is related to the period in time and to the wavevector by c = λ/ T | k | = 2 π/λ. (2.1) where c is the speed of light, i.e. the wavepacket group velocity of light. The electric and magnetic fields are not independent but are linked to one another. Maxwell ’s equations, representing the fundamental mathematical framework of radiation, require a changing electric field to be accompanied by a magnetic field 1 . Both fields are propagating with the same finite speed c . For light in vacuum it is the highest speed possible in nature. 2.2 The electromagnetic spectrum White light is a mixture of many colors. In 1672 this was demonstrated by Isaac Newton who separated the colors of white light with a prism and joined them again with a second prism. Colors are determined by the wavelength. In experiments similar to this well-known example, different colors may be sorted by processes depending on wavelength like refraction or diffraction of light forming the basis of spectrographs. An illustration of the large range of wavelengths of electromagnetic radiation is contained in figure 2.2 showing a frequency and wavelength scale spanning 20 orders of magnitude. The radiation involved ranges from radio waves over infrared and visible light to x-and gamma-rays.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as retarded time (as opposed to advanced time, which is unphysical in light of causality), which adds to the expressions for the electrodynamic electric field and magnetic field. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. At the quantum level, electromagnetic radiation is produced when the wavepacket of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in oscillation, which is responsible for the phenomenon of radiative transition between quantum states of a charged particle. Depending on the circumstances, electromagnetic radiation may behave as a wave or as particles. As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν , where E is the energy of the photon, h = 6.626 × 10 −34 J·s is Planck's constant, and ν is the frequency of the wave. One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer , regardless of the observer's velocity. (This observation led to Albert Einstein's development of the theory of special relativity.) In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
This is manifested in the emission spectrum of nebulae. Today, scientists use this phenomenon to observe what elements a certain star is composed of. It is also used in the determination of the distance of a star, using the red shift. ________________________ WORLD TECHNOLOGIES ________________________ Speed of propagation Any electric charge which accelerates, or any changing magnetic field, produces electromagnetic radiation. Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as retarded time (as opposed to advanced time, which is unphysical in light of causality), which adds to the expressions for the electrodynamic electric field and magnetic field. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. At the quantum level, electromagnetic radiation is produced when the wavepacket of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in oscillation, which is responsible for the phenomenon of radiative transition between quantum states of a charged particle. Depending on the circumstances, electromagnetic radiation may behave as a wave or as particles. As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν , where E is the energy of the photon, h = 6.626 × 10 −34 J·s is Planck's constant, and ν is the frequency of the wave. One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer , regardless of the observer's velocity.
eBook - PDF- Olsen, R.C.(Authors)
- 2007(Publication Date)
The angular frequency v is defined as v ¼ 2 p f . The wavenumber is defined as k ¼ 2 p / l . The period t is the inverse of the frequency because for a wave it must be true that v · t ¼ 2 p or f · t ¼ 1. 2.2 Polarization of Radiation A subtle but important point is that E and B are both vectors. This vector character of EM radiation becomes important when considering the concept of polarization. Familiar as an aspect of expensive sunglasses, polarization appears in both optical observations and radar. A brief illustration of how EM waves propagate becomes necessary at this point. Figure 2.2 shows how the electric and magnetic fields oscillate with respect to one another in an EM wave (in a vacuum). The electric and magnetic fields are perpendicular to one another and to the direction of propagation k . These waves are transverse, as opposed to longitudinal, waves (also termed compressional , e.g., sound waves). Other forms of polarization are possible Figure 2.1 Four cycles of a wave are shown, with wavelength l or period t . The wave has an amplitude A equal to 3. 29 Electromagnetic Basics but harder to illustrate. Linear polarization, as discussed here, is the more common form found in natural environments. Polarization with active radar systems will be illustrated in Chapter 10 (see Fig. 10.0). Radar signals are intrinsically linearly polarized, and the orientation is adjusted according to the mission. The receiver can be adjusted to receive either co-polarized or cross-polarized signals, i.e., either parallel or perpendicular to the transmitted signal, respectively. Optical polarization in nature is relatively subtler. Figure 2.3 shows a pair of color photographs of a building, trees, and blue sky. The two images were taken with a linear optical polarization filter in a pair of perpendicular orientations. The main difference in the images is the Figure 2.2 An electromagnetic wave.
- Sow-Hsin Chen, Michael Kotlarchyk;;;(Authors)
- 2007(Publication Date)
- WSPC(Publisher)
122 Classical Treatment of Electromagnetic Fields and Radiation x y z q f r [ p ] .. B E e r Figure 4.2 Field vectors in the radiation zone of a time-varying electric dipole. or radiation zone . In this region, we only keep terms of order r -1 , and the radial component of the electric field vanishes. The only surviving field components are E θ = B φ = [¨ p ] c 2 r sin θ. (4.126) As shown in Fig. 4.2, E and B are transverse fields in the radiation zone; they can be expressed compactly as B = 1 c 2 r [ ¨ p ] × e r (4.127) E = B × e r . (4.128) These fields transport energy radially outward from the dipole at a rate per unit area determined by the Poynting vector, S : S = c 4 π E × B = parenleftBigg [¨ p ] 2 4 πc 3 r 2 sin 2 θ parenrightBigg e r = c 4 π E 2 e r = c 4 π B 2 e r . (4.129) The power radiated by the dipole per unit solid angle d Ω is dP d Ω =( S · e r ) r 2 = [¨ p ] 2 4 πc 3 sin 2 θ. (4.130) Figure 4.3 displays this sin 2 θ angular distribution for dipole radiation. It also follows Field Due to a Changing Polarization 123 Figure 4.3 Radiation pattern from time-varying dipole. that the total power emitted is P = integraldisplay 4 π dP d Ω d Ω= [¨ p ] 2 4 πc 3 π integraldisplay θ =0 2 π integraldisplay φ =0 ( sin 2 θ ) sin θdθdφ = 2[¨ p ] 2 3 c 3 . (4.131) In the case when the time-variation of the dipole moment is simple harmonic, i.e., [ p ]= p ( t prime )=( p 0 cos ωt prime ) e z , (4.132) it is particularly straightforward to compute the average power emitted, as long as an integral number of cycles is considered. Here, one need not be concerned about the evaluation of p at retarded time t prime since all times are essentially equivalent.
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