GATE EC 2004 Electromagnetics Solution Q 2

GATE EC 2004 Electromagnetics Solution Q 2

If given \overrightarrow E=\left({\widehat a}_x+j{\widehat a}_y\right)e^{jkz-j\omega t} and \overrightarrow H=\left(\frac k{\omega\mu}\right)\left({\widehat a}_y+j{\widehat a}_x\right)e^{jkz-j\omega t} ,the time averaged pointing vector is

(a) null vector

(b) \left(\frac k{\omega\mu}\right){\widehat a}_z

(c) \left(\frac{2k}{\omega\mu}\right){\widehat a}_z

(d) \left(\frac k{2\omega\mu}\right){\widehat a}_z

Ans : a)

Explanation

{\overrightarrow P}_{avg}=\frac12R_e\left[\overrightarrow E\times\overrightarrow H\right] =\frac12R_e\left[\left({\widehat a}_x+j{\widehat a}_y\right)e^{jkz-j\omega t}\times\frac k{\omega\mu}\left({\widehat a}_y-j{\widehat a}_x\right)e^{-jkz+j\omega t}\right] {\overrightarrow P}_{avg}=\frac k{2\mu\omega}\left[0\right]=0

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