Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 130f the amplitude at z = 0 when it arrives at z-100 m). (1) Find a. (2) Suppose the conductivity of the mediumis σ, the dielectric constant is &, and the relative permeability is f,-1 for the medium. Notice that ε eo and μ μμ. Assuming σ<< 2Tfe, prove that simple, approximate expressions for α and β can be (3) Assumes. 2.5. Recall that v μ/ca-37742. Using the above approximation and α found in (1), find ơ Use-/25-1.58. (4) Does the σ found in (3) Justify the use of the approximation? Explain your answer. For quick estimation, you may find a (1/36m)x 10 F/m useful. (5) (Optional, for bonus) What is the phase difference between the magnetic field and the electric field of this wave at this frequency f 1 GHz? Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 130f the amplitude at z = 0 when it arrives at z-100 m). (1) Find a. (2) Suppose the conductivity of the mediumis σ, the dielectric constant is &, and the relative permeability is f,-1 for the medium. Notice that ε eo and μ μμ. Assuming σ