First slide

Intensity of electromagnetic wave

Question

The electric field intensity produced by the radiations coming from 100 W bulb at a 3 m distance is E. The electric field intensity produced by the radiations coming from 50 W bulb at the same distance is

Moderate

A

E/2
B

E
C

$\frac{E}{\sqrt{2}}$
D

$\sqrt{2} E$

Solution

Intensity of electromagnetic wave
$I = (\frac{1}{2} \in_{0} {E_{0}}^{2}) C - - - - - - - (1)$
Here E₀ = Amplitude of electric field intensity. If ‘P’ is power of source, intensity of electromagnetic radiation at a distance ‘r’
from source is
$I = \frac{P}{4 {πr}^{2}} - - - (2);$
From (1) and (2)
$\frac{1}{2} \in_{0} {E_{0}}^{2} C = \frac{P}{4 {πr}^{2}} \Rightarrow P \propto {E_{0}}^{2}; E_{0} \propto \sqrt{P} \sqrt{\frac{P_{2}}{P_{1}}} = \frac{E_{2}}{E_{1}}; \sqrt{\frac{P_{2}}{P_{1}}} = \frac{E_{2}}{E_{1}} \sqrt{\frac{50}{100}} = \frac{1}{\sqrt{2}} = \frac{E_{2}}{E_{1}} \Rightarrow E_{2} = \frac{E_{1}}{\sqrt{2}} = \frac{E}{\sqrt{2}}$

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