6. (i) Derive the following wave equation in a linear, isotropic and homogeneous (LIH) medium of conductivity o, permitt

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6 I Derive The Following Wave Equation In A Linear Isotropic And Homogeneous Lih Medium Of Conductivity O Permitt 1 (266.25 KiB) Viewed 37 times

6. (i) Derive the following wave equation in a linear, isotropic and homogeneous (LIH) medium of conductivity o, permittivity & and permeability μ: V²E-0μ- εμ JE a²E Ət at² = 0. [15 marks] (ii) Hence show that if the field H=ÎH, expj(wt - k z), the associated electric field is given by E = k jσ-ωεμ -|H|Ĵ. [15 marks] (iii) In the case of a non-conducting LIH dielectric medium, the wavenumber k=√√eu. More realistically, a lossy dielectric may attenuate electromagnetic fields through two distinct processes. The first is associated with dielectric polarization and the second with a finite conductivity. This may be modelled by transforming the permittivity into a complex, frequency dependent quantity, such that E = ɛ'-jɛ' -jº. @ Making use of this definition of & and defining jk = a + jß, show that a is an attenuation constant and derive the expression 4+0)-}* α = where &" = & + [30 marks] O @