A radiation is emitted by 1000W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m. The efficiency of the bulb is 1.25%. The value of peak electric field at P is x $\times$ 10$-$1 V/m. Value of x is ___________. (Rounded off to the nearest integer) [Take ${\varepsilon _0} = 8.85 \times {10^{ - 12}}$ C2N$-$1 m$-$2, c = $3 \times {10^8}$ ms$-$1]
Answer (integer)
137
Solution
Intensity of electro magnetic wave is,<br><br>$I = {1 \over 2}c{\varepsilon _0}E_0^2 = {P \over {4\pi {r^2}}}$<br><br>${1 \over 2}4\pi {\varepsilon _0} \times c \times E_0^2 = {P \over {{r^2}}}$<br><br>$${1 \over 2} \times {{3 \times {{10}^5} \times E_0^2} \over {9 \times {{10}^9}}} = {{1000 \times 1.25} \over {{{(2)}^2}}} \times {1 \over {100}}$$<br><br>$$E_0^2 = {{60 \times 1000 \times 1.25} \over {4 \times 100}} = {{125 \times 3} \over 2}$$<br><br>$E_0^2 = {{375} \over 2} = 187.5$<br><br>${E_0} = 13.69$<br><br>${E_0} \approx 137 \times {10^{ - 1}}$ v/m
About this question
Subject: Physics · Chapter: Electromagnetic Waves · Topic: Maxwell's Equations
This question is part of PrepWiser's free JEE Main question bank. 109 more solved questions on Electromagnetic Waves are available — start with the harder ones if your accuracy is >70%.