Practicing Success
Assume that a lamp radiates power P uniformly in all directions. What is the magnitude of electric field strength at a distance r from the lamp? |
$\frac{P}{\pi c \varepsilon_0 r^2}$ $\frac{P}{2 \pi c \varepsilon_0 r^2}$ $\sqrt{\frac{P}{2 \pi \varepsilon_0 r^2 c}}$ $\sqrt{\frac{P}{\pi \varepsilon_0 cr^2}}$ |
$\sqrt{\frac{P}{2 \pi \varepsilon_0 r^2 c}}$ |
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 $\frac{1}{2} \varepsilon_0 E_0^2 c=\frac{P}{4 \pi \mathrm{r}^2}$ $E_0=\sqrt{\frac{2 P}{4 \pi \varepsilon_0 \mathrm{r}^2 c}}=\sqrt{\frac{P}{2 \pi \varepsilon_0 r^2 c}}$ |