Question

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?

• A. $\frac{P}{\pi c{ϵ}_0{r}^2}$
• B. $\frac{P}{2\pi cϵr^2}$
• C. $\sqrt{\frac{P}{2\pi {ϵ}_0{r}^{2}c}}$
• D. $\sqrt{\frac{P}{\pi {ϵ}_{0}c{r}^2}}$

Answer 1

Answer: (C)

Intensity $I=\frac{power}{area}=\frac{p}{4\pi r^2}$
=average energy density $\times$ velocity
$=\frac{1}{2}{ϵ}_0{E}_0^{2}c$
$\therefore E_0=\sqrt{\frac{2P}{4\pi {ϵ}_0{r}^{2}c}}=\sqrt{\frac{P}{2\pi {ϵ}_0{r}^{2}c}}$