Final answer:
The relative dielectric permittivity (εr) of the biological material affects the propagation speed and wavelength of the EM wave. The wave's amplitude decreases as it propagates, with given parameters such as a 2.75 dB/cm decay, a wavevector of 250 rad/m, and affects the calculation of the displacement current in the scenario described.
Step-by-step explanation:
Understanding Electromagnetic Waves in Biological Materials:
When considering a uniform plane electromagnetic (EM) wave propagating inside a biological material, the interaction between the EM field and the material can be described by the wave equation. The electric and magnetic fields (E and B) in an EM wave are always perpendicular to each other and to the direction of wave propagation. In your scenario, the EM wave propagates in the z direction, the electric field (E) is directed along the x-axis, and the magnetic field (B) is directed along the y-axis. Given an electric field amplitude of Eo = 30 mV/m and a frequency (f) of 1.9 GHz, we can explore various properties of the wave in the biological material.
To determine the relative dielectric permittivity (εr) of the biological material, we must account for the decaying amplitude as the wave propagates through the medium. The relative permittivity influences the propagation speed and wavelength of the EM wave. As the wave penetrates the material, its amplitude decreases by 2.75 dB/cm. The wavevector (k) value given at 250 rad/m is related to the relative dielectric permittivity and the speed of light in vacuum (c).
In the case of the plane wave defined by Ex = 0; Ey = Eo cos (kx - wt); Ez = 0 and Bx = 0; By = 0; Bz = Bo cos (kx - wt), the displacement current through a circular cross-sectional tube can be calculated using Maxwell's equations, taking into consideration the rate of change of the electric field within the tube.