Problem 2. A plane-wave propagating in i direction is incident from medium 1 (location: 2 0, = 60; 4 = 10, o = 10 S/m) with a frequency f = 1 GHz. Assume the amplitude of the incident plane-wave electric-field is E. (real quantity). (a) Find the reflection coefficient l' and transmission coefficient I that characterize the reflected and transmitted electric-field intensities respectively at the planar boundary separating the two media. (b) Find an expression for the time-averaged power dissipated in the conducting medium per unit area in terms of the usual parameters. For this calculation, use expressions for time- averaged Poynting vectors for incident, reflected, and transmitted waves. (c) Just like in circuits where the power dissipated in a given circuit is IV, similarly in elec- tromagnetics, the power dissipated (per unit volume) by mobile charges is J.. The time- averaged power dissipated per unit volume in the conducting medium at a given location is Re{]. }. Note that the conductivity of the medium could be used to calculate the conduction current I. To calculate time-averaged power-dissipated per unit area in the conducting medium, you could integrate the above expression through the entire thickness of the medium by using the expression Lrei- }dz. Compute this integral and show that the result is the same as that obtained in part (b). Problem 2. A plane-wave propagating in i direction is incident from medium 1 (location: 2 0, = 60; 4 = 10, o = 10 S/m) with a frequency f = 1 GHz. Assume the amplitude of the incident plane-wave electric-field is E. (real quantity). (a) Find the reflection coefficient l' and transmission coefficient I that characterize the reflected and transmitted electric-field intensities respectively at the planar boundary separating the two media. (b) Find an expression for the time-averaged power dissipated in the conducting medium per unit area in terms of the usual parameters. For this calculation, use expressions for time- averaged Poynting vectors for incident, reflected, and transmitted waves. (c) Just like in circuits where the power dissipated in a given circuit is IV, similarly in elec- tromagnetics, the power dissipated (per unit volume) by mobile charges is J.. The time- averaged power dissipated per unit volume in the conducting medium at a given location is Re{]. }. Note that the conductivity of the medium could be used to calculate the conduction current I. To calculate time-averaged power-dissipated per unit area in the conducting medium, you could integrate the above expression through the entire thickness of the medium by using the expression Lrei- }dz. Compute this integral and show that the result is the same as that obtained in part (b)