Question

The electric field intensity produced by the radiation coming from a $100\text{W}$ bulb at a distance of $3\text{m}$ is $E$. The electric filed intensity produced by the radiation coming from $60\text{W}$ at the same distance is $\sqrt{\frac{x}{5}}E$. Where the value of $x$ is .

Answer 1

Intensity of electromagnetic radiation is given as$$I=\frac{1}{2}C{\epsilon }_0{E}^2$$ Where $E$ is electric field intensity at a point.
So, $E^2\propto$ $I$
Also, $I=\frac{\text{Power}}{\text{Area}}$

So, $E^2\propto \frac{P}{A}$

$E\propto \sqrt{P}$ [at the same distance, $A$ will be the same]

Now, $\frac{E^{\prime }}{E}=\sqrt{\frac{60}{100}}$
$E^{\prime }=\sqrt{\frac{3}{5}}E$
So the value of $x=3$