GATE EC 2011 Electromagnetics Solution Q 5

GATE EC 2011 Electromagnetics Solution Q 5

Consider the following statements regarding the complex pointing vector p for the power radiated by a point source in an infinite homogenous and lossless medium. Re ( \overrightarrow P) denotes the unit real part of \overrightarrow P, S denotes a spherical surface whose centre is at the point source, and \widehat n denotes the unit surface normal on S. Which of the following statements is TRUE?

(a) Re \left(\overrightarrow P\right) remain constant at any radial distance from the source

(b) Re \left(\overrightarrow P\right) increses with incresing radial distance from the source

(c) \oint\limits_sRe\left(\overrightarrow P\right).\widehat ndS remains constant at any radial distance from the source

(d) \oint\limits_sRe\left(\overrightarrow P\right).\widehat ndS decreases with increasing radial distance from the source

Ans : (c)

Explanation

\oint\limits_sRe\left(\overrightarrow P\right).\widehat ndS is the time averaged Poynting vector hence a constant.

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