GATE EC 1998 Electromagnetics Solution Q 6

GATE EC 1998 Electromagnetics Solution Q 6

The time averaged Poynting vector, in W/m2 , for a wave with

$latex \overrightarrow E=24e^{j\left(\omega t+\beta z\right)}{\overrightarrow a}_y\;V/m$

in free space is

(a) -\frac{2.4}\pi{\overrightarrow a}_z

(b) \frac{2.4}\pi{\overrightarrow a}_z

(c) \frac{4.8}\pi{\overrightarrow a}_z

(d) -\frac{4.8}\pi{\overrightarrow a}_z

Ans : a)

Explanation

As wave is travelling in -Z direction, time Averaged Poynting Vector is given by

P_{avg}=\frac1{2\eta_0}\left|E\right|^2\left(-{\overline a}_z\right)

Here, \left|\overrightarrow E\right|\;=\;24and  \eta=\eta_0=120\pi\Omega

P_{avg}=\frac{\left(24\right)^2}{2\left(120\pi\right)}\left(-{\overline a}_z\right) P_{avg}=-\frac{2.4}\pi{\overrightarrow a}_z\;W/m^2

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