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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?
Electromagnetic Waves
Solution:
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
$I=c=\frac{1}{2}\varepsilon_{0}E^{2}_{0}c\,...\left(ii\right)$
Equating \left(i\right) and $\left(ii\right)$, we get
$\frac{1}{2}\varepsilon_{0}E^{2}_{0}c=\frac{P}{4\pi r^{2}}$
$E_{0}=\sqrt{\frac{2P}{4\pi\varepsilon_{0}r^{2}c}}=\sqrt{\frac{P}{2\pi\varepsilon_{0}r^{2}c}}$