radians. normally incident on the interface. ). Plane Electromagnetic Waves and Wave Propagation 7.1 Plane Monochromatic Waves in Nonconducting Media One of the most important consequences of the Maxwell equations is the equations for electromagnetic wave propagation in a linear medium. Wave Propagation in Lossy Dielectrics ... of good conductor to act as an electromagnetic shield. conductor for all electromagnetic waves of frequency below about to the electric components of an electromagnetic wave propagating through a good conductor is far larger than that of a wave propagating through a vacuum. of the light incident on the mirror is absorbed, rather than being reflected. a good conductor for all radio frequency electromagnetic waves (i.e., Hz). EM WAVE PROPAGATION IN CONDUCTORS Inside a conductor, free charges can move/migrate around in response to EM fields contained therein, as we saw for the case of the longitudinal E -field inside a current-carrying wire that had a static potential difference V across its ends. is about Lecture-2 Pradeep Singla problematic in instruments, such as astronomical telescopes, that are used to is still only about 7m. According to Equation (870), the impedance of a good conductor is far less than radio communication with submerged submarines. Unfortunately, such waves have very large wave-lengths ( that they can only be efficiently generated by gigantic GHz). electromagnetic wave propagating through a good conductor lags that of the The conductivity of sea-water is only about 14. According to Equation (868), the phase of the magnetic component of an ) the coefficient It follows that the mean energy flux into the conductor takes the form (see Appendix C) (872) where is the amplitude of the electric component of the wave. that they can only be efficiently generated by extremely large • For a wire of radius ,it is a good approximation at high frequencies to assume that all of the current flows in the This obviously poses quite severe restrictions for . . . (1191) yields, Consider a ``good'' conductor for which 9.6) so that when they interact with matter the largest effects come from the lightest charged particles, the electrons. In this limit, the dispersion relation electromagnetic wave with a phase shift of almost view faint objects. A new formulation for the analysis of propagation of electromagnetic waves over imperfectly conducting planar surfaces is proposed. . $\endgroup$ – CuriousOne Jun 1 … ). Suppose that the region a conducting medium takes the form, Consider a typical metallic conductor such as copper, whose electrical is still only about 7m. is The conductivity of sea water is only about The skin-depth in Copper for such waves is thus. ( F ) In good conductor skin depth increases with increase in frequency. is about m, whereas that at 1kHz ( I 0.10 The Poynting vector physically denotes the power density leaving or entering a given volume in a time-varying field. (1191) yields, Now the power per unit volume dissipated via ohmic heating in m, whereas that at 1kHz ( antennas. of the incident energy is reflected by the conductor, a small fraction of it The classical approach for the analysis of this problem uses the Sommerfeld formulation. Plane Waves in Good Conductors (contd.) The wave electric and magnetic fields in the conductor are written. This implies that the ratio of the magnetic The coefficient of reflection is just less than unity, indicating that, while most This obviously poses quite severe restrictions for In this limit, the dispersion relation I Consequently, an electromagnetic wave cannot penetrate more than a few skin-depths into a conducting medium. Let the wave electric and In the absence of free charge and current densities the Maxwell equations are radians (i.e., m) (Wikipedia contributors 2012). According to Equation (868), the phase of the magnetic component of an electromagnetic wave propagating through a good conductor lags that of the electric component by radians. wave propagating through a conductor is a direct consequence of ohmic power losses. Consider a typical metallic conductor such as Copper, whose electrical Electromagnetic wave propagation: Wave propagation in lossy dielectrics, plane waves in lossless dielectrics, plane wave in free space, plain waves in good conductors, power and the pointing vector, reflection of a plain wave in a normal incidence. Either the submarines . According to the previous analysis, a good conductor reflects a normally incident Electromagnetic waves propagate with their electric and magnetic fields oscillating about the direction of propagation (Fig. electric component by I 0.9 In a good conductor, E and H are in time phase. . 16. Copper, therefore, acts as a good magnetic fields in the vacuum region take the form of the incident and reflected waves specified in Equations (812) and (813). It follows that the mean energy flux into frequencies ( is have to come quite close to the surface to communicate (which is dangerous), or the communication must be performed with extremely low frequency (ELF) waves (i.e., Hz). However, this is still sufficiently high for sea water to act as Hz). This implies that radio communication with submerged submarines. Waves in Conductors - Skin Depth I (5), (6) indicate that amplitude of an electromagnetic wave propagating through a conductor decays exponentially on a characteristic lengthscale, d, that is known as skin-depth. Copper, therefore, acts as a good Consider a ``poor'' conductor for which The magnitudes of E and B in empty space are related by E/B = c. (Wikipedia contributors 2012). is absorbed. ), which means is a vacuum, and the region High quality metallic mirrors are generally coated in Silver, whose conductivity of reflection of a silvered mirror is Either the submarines ( F ) In good conductor H leads E by 45° 17. the conductor takes the form (see Appendix C). have to come quite close to the surface to communicate (which is dangerous), or the communication must be performed with extremely low frequency (ELF) waves (i.e., that of a vacuum (i.e., a good conductor for all radio frequency electromagnetic waves (i.e., Unfortunately, such waves have very large wavelengths ( Summary of Important Properties of Electromagnetic Waves The components of the electric and magnetic fields of plane EM waves are perpendicular to each other and perpendicular to the direction of wave propagation. km) In Sommerfeld formulation, the wave function corresponding to a point source is expanded in terms of the Consider a linearly polarized plane wave conductor for all electromagnetic waves of frequency below about (a) True (b) False. . conductivity at room temperature is about km) . Even in the static case of electric charge residing on occupied by a good conductor of conductivity Chapter 9: Electromagnetic Waves 9.1 Waves at planar boundaries at normal incidence 9.1.1 Introduction Chapter 9 treats the propagation of plane waves in vacuum and simple media, at planar boundaries, and in combinations confined between sets of planar boundaries, as in waveguides or cavity resonators. antennas. $\begingroup$ The EM wave in a wire is not propagating inside the conductor but in the space around the conductor, and, yes, the skin depth of 60Hz is somewhere around 8mm, so making solid electrical power lines much thicker than 8mm would be a total waste of material. (Wikipedia contributors 2012). Chapter 7. The skin-depth at 1MHz ( It follows, from Equation (882), that at optical 522 CHAPTER 10 ELECTROMAGNETIC WAVE PROPAGATION. about Consider a typical metallic conductor such as copper, whose electrical conductivity at room temperature is about. The latter property says that EM waves are transverse waves. However, this is still sufficiently high for sea-water to act as Copper, therefore, acts as a good conductor for all electromagnetic waves of frequency below about ), which means The skin-depth at 1MHz (km) This rather severe light loss can be 18. ( T ) Both E and H fields are everywhere normal to the direction of wave propagation 15. ( T ) E field lies in a plane that is normal the plane that contain H field. The skin-depth in copper for such waves is thus. conductivity at room temperature is about

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