Assume that a lamp radiates power P uniformly in all directions. What…

A lamp radiates light uniformly in all directions. Therefore, intensity I at a distance r from the lamp is

$I=\frac{\text { Power }}{\text { Area }}=\frac{P}{4 \pi r^2}$                     (i)

Intensity of the electromagnetic wave is

$I=<u>c=\frac{1}{2} \varepsilon_0 E_0^2 c$            (ii)

Equating (i) and (ii), we get

$\frac{1}{2} \varepsilon_0 E_0^2 c=\frac{P}{4 \pi \mathrm{r}^2}$

$E_0=\sqrt{\frac{2 P}{4 \pi \varepsilon_0 \mathrm{r}^2 c}}=\sqrt{\frac{P}{2 \pi \varepsilon_0 r^2 c}}$