The electric field intensity produced by the radiations coming from a 200 W bulb at 6 m distance is E. What is the electric field intensity produced by the radiations coming from 100 W bulb at the same distance?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{E}{\sqrt{2}}$
The electric field intensity ($\vec E$) produced by electromagnetic radiation is related to the power (P) of the source and the distance (r) as follows -
Average power per unit area, or intensity (I) of a spherical wave is given by -
$I=\frac{P}{4πr^2}$ ...(1)
and,
Intensity of the wave is related to the electric field magnetic as -
$I∝E^2$ ...(2)
from (1) and (2) we get,
$E^2∝P$
$⇒E∝\sqrt{P}$
∵ Let $E_1$ be the electric field intensity due to the 200 W bulb and $E_2$ be electric field intensity due to 100W bulb.
$⇒\frac{E_1}{E_2}=\sqrt{\frac{200}{100}}⇒E_2=\frac{E_1}{\sqrt{2}}$