A person with a receiver is 5 Km away from the transmitter. What is the distance that this person must move further to detect a 3-dB decrease in signal strength?

Distilled water at $${25^ \circ }C$$ is characterized by $$\sigma = 1.7 \times {10^{ - 4}}$$ mho/m and $$ \in = 78{ \in _0}$$ at a frequency of $$3 GHz$$. Its loss tangent $$\tan \delta $$ is

A plane wave is characterized by $$$\overrightarrow E = \left( {0.5\mathop x\limits^ \cap + \mathop y\limits^ \cap \,{e^{j\pi /2}}} \right){e^{j\omega t - jkz}}.$$$

This wave is

Consider a parallel plate waveguide with plate separation d as shown in Fig. The electric and magnetic fields for the TEM mode are given by $${E_x} = \,{E_0}\,\,{e^{ - j\,k\,z + j\,\omega \,t}},\,{H_y} = {{{E_0}} \over \eta }\,{e^{ - j\,k\,z + j\,\omega \,t}}$$

Where $$k = \,\,\eta \,\omega \,\, \in $$
(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d
(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.
(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.