Question

7. A linearly polarized 10 GHz electromagnetic plane wave is normally incident on surface of mercury. At what depth in the mercury will the electric field ofthe wave be reduced to 10% of its incident value? Resistivity of mercury 106 ohm meters.

Answer 1

Vertical-bar E^- Vertical-bar = E_0 e^- alpha z: amplitude of the magnitude of E^- field travelling in z^- - direction. f = 10 GH , sigma = 1/p = 10^6 Ohm/m (conductivity of the medium) At z = 0, the medium mercury starts and At z = d, it's amplitude reduces to 10% of its incident wave. loss tangent = sigma/w sigma = 10^6/2 pi times 10^10 times 10^-9/36 pi = 18 times 10^5 > > 1 Therefore mercury is good conductor at f = 10 GHZ alpha = squareroot pi f mu sigma (for Good conductors) = squareroot pi times 10^10 times 4 pi times 10^-7 times 10^6 [mu = mu_0 = pi times 10^-7] = squareroot (2pi)^2 times 10^9 = 2 pi times squareroot 10 times 10^4 NP/m At z = d, Vertical-bar E^- Vertical-bar = 0.1 E_o = E_o e^- alpha d rightarrow 0.1 = e^-alpha d rightarrow (n (0.1) = -alpha d rightarrow d = -ln 0.1/alpha = 11.588 mu m