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  4. A lamp emits monochromatic green light uniformly in all directions. The lamp is 3 % efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly :

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Q. A lamp emits monochromatic green light uniformly in all directions. The lamp is $3\%$ efficient in converting electrical power to electromagnetic waves and consumes $100 \,W$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5 \,m$ from the lamp will be nearly :

JEE MainJEE Main 2014Electromagnetic Waves

Solution:

$I =< u > c =\frac{ P }{4 \pi r ^{2}}$
$\frac{\epsilon_{0} \in_{0}^{2}}{2} C =\frac{ P }{4 \pi r ^{2}}$
$\epsilon_{0}^{2}=\frac{ P }{2 \pi r ^{2} \epsilon_{0} C }$
$\epsilon_{0}=\sqrt{\frac{ P }{2 \pi r ^{2} \in_{0} C }}$
$=\sqrt{\frac{3}{2 \pi(5)^{2} \times 8.85 \times 10^{-12} \times 3 \times 10^{8}}}$
$\epsilon_{0}=2.68\,volt / metre$