A point source of electromagnetic radiation has an average power output of \(960 \mathrm{~W}\). The peak…

A point source of electromagnetic radiation has an average power output of \(960 \mathrm{~W}\). The peak value of the electric field at a distance \(400 \mathrm{~cm}\) from the source is
  1. \(60 \mathrm{Vm}^{-1}\)
  2. \(120 \mathrm{Vm}^{-1}\)
  3. \(30 \mathrm{Vm}^{-1}\)
  4. \(180 \mathrm{Vm}^{-1}\)

Solution

Given, average power output, \(P=960 \mathrm{~W}\) Distance, \(r=400 \mathrm{~cm}=4 \mathrm{~m}\) Intensity of \(E M\) waves is given by \(\begin{aligned} I & =\frac{P}{4 \pi r^2}=\frac{1}{2} \varepsilon_0 E_0^2 c \Rightarrow E_0^2=\frac{P}{2 \pi r^2 \varepsilon_0 c} \\ \therefore \quad E & =\sqrt{\frac{P}{2 \pi r^2 \varepsilon_0 c}} \\ & =\sqrt{\frac{960}{2 \times 3.14 \times 4^2 \times 8.85 \times 10^{-12} \times 3 \times 10^8}} \\ & =\sqrt{0.36 \times 10^4}=0.6 \times 10^2=60 \mathrm{Vm}^{-1} \end{aligned}\)

Asked in: AP EAMCET 2019 (22 Apr Shift 1)

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