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  •  A lamp emits monochromatic green light uniformly in all directions. The lamp is 3%  efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amp

 A lamp emits monochromatic green light uniformly in all directions. The lamp is 3%  efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude ( in V/m) of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly :    

 

Option: 1

2.68


Option: 2

1.34


Option: 3

4.02


Option: 4

5.36


Answers (1)

best_answer

As we have learned in

The intensity of EM wave -

I = \frac{1}{2} \epsilon _{o} E_{o}^{2}c

- wherein

\epsilon _{o} = Permittivity of free space

E _{o} = Electric field amplitude

c = Speed of light in vacuum

The wavelength of monochromatic green light = 5.5 \times 10^{-5} cm

I = \frac{P}{A}= \frac{100\times \left ( \frac{3}{100} \right )}{4\times \pi \times \left ( 5 \right )^{2}}= \frac{3}{100\pi }Wm^{-2}

Now, half of this intensity (1) belongs to the electric field and half of that magnetic field

\frac{I}{2}= \frac{1}{4}\epsilon _{0}E^{2}c

\Rightarrow E_{0}= \sqrt{\frac{2I}{\epsilon _{0}c}}

E_{0}= \sqrt{\frac{2\times \left ( \frac{3}{100\pi } \right )}{\left ( 8.85\times 10^{-12} \right )\times \left ( 3\times 10^{8} \right )}}

E_{0}= \sqrt{7.2} \Rightarrow E_{0} = 2.68 \frac{V}{m}

Posted by

Ritika Harsh

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