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?

$\frac{E}{\sqrt{2}}$

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.

$⇒\frac{E_1}{E_2}=\sqrt{\frac{200}{100}}⇒E_2=\frac{E_1}{\sqrt{2}}$