Question

A radiation is emitted by $1000\text{W}$ bulb, and it generates electric field and magnetic field at $P$, placed at a distance of $2\text{m}$. The efficiency of the bulb is $1.25$%. The value of peak electric field at $P$ is $x\times {10}^{-1}\text{V/m}$. Value of $x$ is __________. $($Rounded-off to the nearest integer$)$
$[$Take ${ϵ}_o=8.85\times {10}^{-12}{\text{C}}^2{\text{/Nm}}^2,c=3\times {10}^8\text{m/s}]$

Answer 1

Intensity of electromagnetic wave,

$I=\frac{1}{2}c{ϵ}_o{E}_o^2=\frac{P}{4\pi r^2}$

$\Rightarrow E_o^2=\frac{P}{2\pi r^{2}c{ϵ}_o}$

$\Rightarrow E_o^2=\frac{1000\times 1.25}{100\times 2\pi \times 2^2\times 3\times {10}^8\times 8.85\times {10}^{-12}}$

$\Rightarrow E_o^2=187.42$

$\Rightarrow E_o=13.7\text{V/m}=137\times {10}^{-1}\text{V/m}$