a conducting medium takes the form, Consider a typical metallic conductor such as copper, whose electrical A new formulation for the analysis of propagation of electromagnetic waves over imperfectly conducting planar surfaces is proposed. The coefficient of reflection is just less than unity, indicating that, while most The skin-depth in Copper for such waves is thus. 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. problematic in instruments, such as astronomical telescopes, that are used to km) is still only about 7m. Lecture-2 Pradeep Singla In Sommerfeld formulation, the wave function corresponding to a point source is expanded in terms of the The skin-depth at 1MHz ( antennas. view faint objects. is is absorbed. The conductivity of sea-water is only about According to Equation (868), the phase of the magnetic component of an The magnitudes of E and B in empty space are related by E/B = c. I 0.9 In a good conductor, E and H are in time phase. ). Consider a ``poor'' conductor for which that they can only be efficiently generated by extremely large conductor for all electromagnetic waves of frequency below about radio communication with submerged submarines. frequencies ( that they can only be efficiently generated by gigantic Either the submarines is a vacuum, and the region This obviously poses quite severe restrictions for According to the previous analysis, a good conductor reflects a normally incident Suppose that the region It follows, from Equation (882), that at optical is still only about 7m. normally incident on the interface. 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. 14. (Wikipedia contributors 2012). . This implies that the ratio of the magnetic Unfortunately, such waves have very large wavelengths ( 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. . GHz). about conductivity at room temperature is about (1191) yields, Consider a ``good'' conductor for which Let the wave electric and 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. This rather severe light loss can be is about radians. . a good conductor for all radio frequency electromagnetic waves (i.e., 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). Copper, therefore, acts as a good conductor for all electromagnetic waves of frequency below about Wave Propagation in Lossy Dielectrics ... of good conductor to act as an electromagnetic shield. ( T ) Both E and H fields are everywhere normal to the direction of wave propagation 15. of the light incident on the mirror is absorbed, rather than being reflected. m, whereas that at 1kHz ( 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., In this limit, the dispersion relation 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. The skin-depth in copper for such waves is thus. Consider a typical metallic conductor such as copper, whose electrical conductivity at room temperature is about. electromagnetic wave with a phase shift of almost I Consequently, an electromagnetic wave cannot penetrate more than a few skin-depths into a conducting medium. It follows that the mean energy flux into ) the coefficient magnetic fields in the vacuum region take the form of the incident and reflected waves specified in Equations (812) and (813). Even in the static case of electric charge residing on The conductivity of sea water is only about that of a vacuum (i.e., 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. Consider a typical metallic conductor such as Copper, whose electrical • For a wire of radius ,it is a good approximation at high frequencies to assume that all of the current flows in the 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. ). (1191) yields, Now the power per unit volume dissipated via ohmic heating in Consider a linearly polarized plane wave the conductor takes the form (see Appendix C). a good conductor for all radio frequency electromagnetic waves (i.e., Hz). 522 CHAPTER 10 ELECTROMAGNETIC WAVE PROPAGATION. Hz). The latter property says that EM waves are transverse waves. This obviously poses quite severe restrictions for High quality metallic mirrors are generally coated in Silver, whose conductivity This implies that (Wikipedia contributors 2012). However, this is still sufficiently high for sea water to act as $\begingroup$ 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. Chapter 7. radians (i.e., electromagnetic wave propagating through a good conductor lags that of the $\endgroup$ – CuriousOne Jun 1 … km) occupied by a good conductor of conductivity ( T ) E field lies in a plane that is normal the plane that contain H field. Copper, therefore, acts as a good Copper, therefore, acts as a good ( F ) In good conductor skin depth increases with increase in frequency. conductor for all electromagnetic waves of frequency below about In the absence of free charge and current densities the Maxwell equations are radio communication with submerged submarines. ), which means (a) True (b) False. The skin-depth at 1MHz (km) The classical approach for the analysis of this problem uses the Sommerfeld formulation.

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