Attenuation and propagation of electromagnetic waves in conductors, Essays (university) of Electromagnetism and Electromagnetic Fields Theory

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ELECTRICAL AND ELECTRONICS ENGINEERING

Attenuation and

propagation of

electromagnetic

waves in conductors

1)ELECTROMAGNETIC WAWES

Definition

Electromagnetic radiation is one of the many ways that energy travels through space. The heat from a burning fire, the light from the sun, the X-rays used by your doctor, as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation. While these forms of energy might seem quite different from one another, they are related in that they all exhibit wavelike properties. If you’ve ever gone swimming in the ocean, you are already familiar with waves. Waves are simply disturbances in a particular physical medium or a field, resulting in a vibration or oscillation. The swell of a wave in the ocean, and the subsequent dip that follows, is simply a vibration or oscillation of the water at the ocean’s surface. Electromagnetic waves are similar, but they are also distinct in that they actually consist of 2 waves oscillating perpendicular to one another. One of the waves is an oscillating magnetic field; the other is an oscillating electric field. This can be visualized as follows: Basic properties of waves: Amplitude, wavelength, and frequency The vertical distance between the tip of a crest and the wave’s central axis is known as its amplitude. The horizontal distance between two consecutive troughs or crests is known as the

and hence find: Similarly: In both equations, on the right-hand side the first term is derived from the conduction current and the second term from the displacement current. As before, a linearly-polarized plane wave travelling along the z-axis could have as its electric vector:

Propagation

where Ɛ is the dielectric constant of the medium. It follows, from the above equations, that Looking for a wave-like solution of the form we obtain the dispersion relation Consider a ``poor'' conductor for which In this limit, the dispersion relation yields.

Where And, Thus, we conclude that the amplitude of an electromagnetic wave propagating through a conductor decays exponentially on some length-scale ,which is termed the skin-depth. Note, from last equation, that the skin-depth for a poor conductor is independent of the frequency of the wave. Note, also, that equation for a poor conductor, indicating that the wave penetrates many wave-lengths into the conductor before decaying away. Consider a ``good'' conductor for In this limit, the dispersion relation yields. Substitution into Eq. It can be seen that the skin-depth for a good conductor decreases with increasing wave frequency. The fact indicates that the wave only penetrates a few wave-lengths into the conductor before decaying away. Now the power per unit volume dissipated via ohmic heating in a conducting medium takes the form for a good conductor. the mean electromagnetic power flux into the region z>0 takes the form It is clear, from a comparison of the previous two equations, that all of the wave energy which flows into the region z>0 is dissipated via ohmic heating. We thus conclude that the attenuation of an electromagnetic wave propagating through a conductor is a direct consequence of ohmic power losses.

There are two general ways of acoustic energy losses: absorption and scattering, for instance light scattering. Ultrasound propagation through homogeneous media is associated only with absorption and can be characterized with absorption coefficient only. Propagation through heterogeneous media requires taking into account scattering. Fractional derivative wave equations can be applied for modeling of lossy acoustical wave propagation, see also acoustic attenuation and Ref. Attenuation decreases the intensity of electromagnetic radiation due to absorption or scattering of photons. Attenuation does not include the decrease in intensity due to inverse-square law geometric spreading. Therefore, calculation of the total change in intensity involves both the inverse-square law and an estimation of attenuation over the path. The primary causes of attenuation in matter are the photoelectric effect, compton scattering, and, for photon energies of above 1.022 MeV, pair production.