The distance (in meters) a wave has to propagate in a medium havi

SOLUTION

Concept:

The amplitude of E.M wave when it propagates through a lossy medium is given by:

\(E = {E_0}{e^{ - \alpha z}}\)

α = attention factor which is the inverse of the skin depth (δ), i.e.

\(\alpha= \frac{1}{{skin\;depth\;\left( δ \right)}}\)

Application:

\(\alpha = \frac{1}{{0.1}} = 10\;{m^{ - 1}}\)

E = E₀ e ^-αz

\(\frac{E}{{{E_0}}} = {e^{ - \alpha z}}\)

\(20\log \left( {\frac{E}{{{E_0}}}} \right) = 20\log \left( {{e^{ - \alpha z}}} \right)\)

For the wave to attenuate by 20 dB, we can write:

\(-20= 20\log \left( {{e^{ - \alpha z}}} \right)\)

-1 = log(e^-αz)

e^-αz = (10)^-1

e-αz = 0.1

αz = 2.302

\(z = \frac{{2.302}}{\alpha } = \frac{{2.302}}{{10}}\)