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GATE ECE 2011 | Question-14

Consider the following statements regarding the complex Poynting vector $\vec{P}$ for the power radiated by a point source in an infinite homogeneous and lossless medium. $\operatorname{Re}(\vec{P})$ denotes the real part of $\vec{P}, S$ denotes a spherical surface whose centre is at the point source, and $\hat{n}$ denotes the unit surface normal on $S$. Which of the following statements is TRUE?

  1. $\operatorname{Re}(\vec{P})$ remains constant at any radial distance from the source
  2. $\operatorname{Re}(\vec{P})$ increases with increasing radial distance from the source
  3. $\oint \oint_S \operatorname{Re}(\vec{P}) . \hat{n} \; dS$ remains constant at any radial distance from the source
  4. $\oint \oint_S \operatorname{Re}(\vec{P}) . \hat{n} \; dS$ decreases with increasing radial distance from the source
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