Question

The magnetic fied associated with a uniform plane wave propagating in the +z direction in free space is given by
$\overrightarrow{H}=0.12\cos (6\pi \times {10}^{7}t-0.7\pi z)\hat{a}yA/m$
The time-average power flow (in mW) across a surface of area $1m^2$ in the z= 0 plane is.____

• A. 987
• B. 2714
• C. 2569
• D. 1345

Answer 1

The correct option is B 2714

$Given:\overrightarrow{H}=0.12\cos (6\pi \times {10}^{7}t-0.2\pi z){\hat{a}}_{y}A/m$
Direction ofpropogation : +z
$H_0=0.12A/m$
$\eta ={\eta }_0=120\pi \left(or\right)377\Omega$
Time averaged power density,
${\overrightarrow{W}}_{avg}=\frac{1}{2}{\eta }_o{H}_0^2\left({\hat{a}}_z\right)$
${\overrightarrow{W}}_{avg}=\frac{1}{2}\left(120\pi \right)\left(0.12{)}^2{\hat{a}}_z\right)$
Average power crossing the area,
$P_{avg}={\overrightarrow{W}}_{avg}S{\hat{a}}_z(\because z=0Plane)$
$\text{Area}S=1m^2$
$P_{avg}=60\pi \left(0.12{)}^2{\hat{a}}_z\right(1){\hat{a}}_z$
= 2.714 W
$\therefore P_{avg}=2714mW$