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

The intensity of radiation from a bulb at distance $$r$$ is $$I = \frac{P}{4\pi r^2}$$, where $$P$$ is the power. The relationship between electric field amplitude and intensity is $$I = \frac{1}{2}\varepsilon_0 c E_0^2$$, so $$E_0 \propto \sqrt{I} \propto \sqrt{P}$$ at a fixed distance.

For the 100 W bulb at 3 m, the electric field intensity is $$E$$. For the 60 W bulb at the same distance, the electric field intensity is $$E' = E\sqrt{\frac{60}{100}} = E\sqrt{\frac{3}{5}}$$.

We are told $$E' = \sqrt{\frac{x}{5}}\,E$$. Comparing, $$\sqrt{\frac{x}{5}} = \sqrt{\frac{3}{5}}$$, which gives $$x = 3$$.