Q. 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) $\frac{P}{\pi c\varepsilon_{0}r^{2}}$
B) $\frac{P}{2\pi c\varepsilon r^{2}}$
C) $\sqrt{\frac{P}{2\pi\varepsilon_{0}r^{2}c}}$
D) $\sqrt{\frac{P}{\pi\varepsilon_{0}cr^{2}}}$
Explanation
(c) Intensity $I = \frac{pressure}{area} = \frac{p}{4\pi r^{2}}$
=average energy density $\times$ velocity
$= \frac{1}{2}\varepsilon_{0}E_{0}^{2}c$
$\therefore E_{0} = \sqrt{\frac{2P}{4\pi\varepsilon_{0}r^{2}c}} = \sqrt{\frac{P}{2\pi\varepsilon_{0}r^{2}c}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.