Question

Assume that a lamp radiates power ${}^{\prime }{P}^{\prime }$ uniformly in all directions. What is the magnitude of electric field strength at a distance $r$ from the lamp?

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

Answer 1

Answer: (C)

A lamp radiates light uniformly in all directions. Therefore, intensity I at a distance r from the lamp is
$I=\frac{Power}{Area}=\frac{P}{4\pi r^2}...\left(i\right)$
Intensity of the electromagnetic wave is
$I=c=\frac{1}{2}{\epsilon }_0{E}_0^{2}c...\left(ii\right)$
Equating \left(i\right) and $\left(ii\right)$, we get
$\frac{1}{2}{\epsilon }_0{E}_0^{2}c=\frac{P}{4\pi r^2}$
$E_0=\sqrt{\frac{2P}{4\pi {\epsilon }_0{r}^{2}c}}=\sqrt{\frac{P}{2\pi {\epsilon }_0{r}^{2}c}}$