JEE Main · 2021 · 17 Mar 2021 · Shift 2 · EM Waves

The intensity of electromagnetic radiation is proportional to the square of the electric field: $I\propto E^2$. Also, intensity is proportional to power and inversely proportional to the square of distance: $I\propto \frac{P}{r^2}$. For the same distance, $\frac{I_2}{I_1}=\frac{P_2}{P_1}=\frac{60}{100}=\frac{3}{5}$. Since $I\propto E^2$, we have $\frac{E_2^2}{E_1^2}=\frac{3}{5}$, so $\frac{E_2}{E_1}=\sqrt{\frac{3}{5}}$. Given $E_1=E$ and $E_2=\sqrt{\frac{x}{5}}E$, we have $\sqrt{\frac{x}{5}}=\sqrt{\frac{3}{5}}$, giving $x=3$.