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

Answer 1

Answer: (C)

Intensity $I=\frac{power}{a r e a}=\frac{p}{4 \pi r^{2}}$
=average energy density $\times $ velocity
$=\frac{1}{2}\epsilon _{0}E_{0}^{2}c$
$\therefore E_{0}=\sqrt{\frac{2 P}{4 \pi \epsilon _{0} r^{2} c}}=\sqrt{\frac{P}{2 \pi \epsilon _{0} r^{2} c}}$