An elliptically polarized wave travelling in the position Z-direction in air has x and y components

E_X = 3 sin (ωt - βz) V/m

E_Y = 6 sin (ωt - βz + 75°) V/m

If the characteristic impedance of air is 360 Ω, the average power per unit area conveyed by the wave is

Concept:-

The average power per unit area conveyed by the wave is given by

\(\rho = \frac{1}{2}\frac{{E_0^2}}{\eta }\)

= \(\frac{1}{2}\eta H_0^2\) W/m²

Where η = Characterstick impedance.

Calculation:

Given E_x = 3 sin (ωt – βz) v/m

E_y = 6 sin (ωt – βz + 75°) v/m

η = 360 Ω

Since E_x and E_y are mutually orthogonal vector So

\({E_0} = \sqrt {E_x^2 + E_y^2} \)

\(\sqrt {{3^2} + {6^2}} \)

= \(\sqrt {45} \)

Average power per unit Area (P_avg) = \(\frac{1}{2}\frac{{E_0^2}}{\eta }\)

= \(\frac{1}{2}\frac{{45}}{{360}}\)

= 62.5 × 10^-3 W/m²

= 62.5 mW/m²