Question

The $\overrightarrow{H}$ field (in A/m) of a plane wave propagating in free space is given by

$\overrightarrow{H}=\hat{x}\frac{5\sqrt{3}}{{\eta }_0}cos(\omega t-\beta z)+\hat{y}\frac{5}{{\eta }_0}sin(\omega t-\beta z+\frac{\pi }{2})$

The time average power flow density in watts is

Answer 1

Ans : (d)

For free space,

$P=\frac{E^2}{2{\eta }_0},E={\eta }_{0}H$

$P=\frac{{\eta }_0^2{H}^2}{2{\eta }_0}=\frac{{\eta }_0{H}^2}{2}$

$H=\frac{1}{{\eta }_0}\sqrt{(5\sqrt{3}{)}^2+(5{)}^2}=\frac{10}{{\eta }_0}$

$P=\frac{{\eta }_0}{2}\times \frac{100}{{\eta }_0^2}=\frac{50}{{\eta }_0}watts$