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Electromagnetic Waves question

2023 · 30 Jan · Shift 2 · Q54
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  5. /2023 · 30 Jan · Shift 2 · Q54

Electromagnetic Waves question

2023 · 30 Jan · Shift 2 · Q54

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
A point source of 100 W100 \mathrm{~W}100 W emits light with 5%5 \%5% efficiency. At a distance of 5 m5 \mathrm{~m}5 m from the source, the intensity produced by the electric field component is:
  1. A
    140πWm2\frac{1}{40 \pi} \frac{W}{m^2}40π1​m2W​
  2. B
    110πWm2\frac{1}{10 \pi} \frac{W}{m^2}10π1​m2W​
  3. C
    120πWm2\frac{1}{20 \pi} \frac{W}{m^2}20π1​m2W​
  4. D
    12πWm2\frac{1}{2 \pi} \frac{W}{m^2}2π1​m2W​
View written solutionFree

Correct answer: A

  1. Useful power emitted as light

The source has total power 100 W100\,\text{W}100W and emits light with 5%5\%5% efficiency.

So, radiant power in the form of light is

Plight=0.05×100=5 WP_{\text{light}} = 0.05 \times 100 = 5\,\text{W}Plight​=0.05×100=5W

  1. Intensity at distance r=5 mr=5\,\text{m}r=5m

For a point source radiating uniformly in all directions,

Itotal=Plight4πr2I_{\text{total}} = \frac{P_{\text{light}}}{4\pi r^2}Itotal​=4πr2Plight​​

Substituting values:

Itotal=54π(5)2=5100π=120π W/m2I_{\text{total}} = \frac{5}{4\pi (5)^2} = \frac{5}{100\pi} = \frac{1}{20\pi}\,\text{W/m}^2Itotal​=4π(5)25​=100π5​=20π1​W/m2

  1. Intensity due to electric field component

In an electromagnetic wave, the energy is equally shared by electric and magnetic fields.

Hence, intensity associated with the electric field component is

IE=12Itotal=12×120π=140π W/m2I_E = \frac{1}{2} I_{\text{total}} = \frac{1}{2}\times \frac{1}{20\pi} = \frac{1}{40\pi}\,\text{W/m}^2IE​=21​Itotal​=21​×20π1​=40π1​W/m2

  1. Match with options

140π W/m2\boxed{\frac{1}{40\pi}\,\text{W/m}^2}40π1​W/m2​

So the correct option is A.

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