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Electromagnetic Waves question

2022 · 28 Jul · Shift 2 · Q54
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  5. /2022 · 28 Jul · Shift 2 · Q54

Electromagnetic Waves question

2022 · 28 Jul · Shift 2 · Q54

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
Sun light falls normally on a surface of area 36 cm236 \mathrm{~cm}^{2}36 cm2 and exerts an average force of 7.2×10−9 N7.2 \times 10^{-9} \mathrm{~N}7.2×10−9 N within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is
  1. A
    25.92×102 W/cm225.92 \times 10^{2} \mathrm{~W} / \mathrm{cm}^{2}25.92×102 W/cm2
  2. B
    8.64×10−6 W/cm28.64 \times 10^{-6} \mathrm{~W} / \mathrm{cm}^{2}8.64×10−6 W/cm2
  3. C
    6.0 W/cm26.0 \mathrm{~W} / \mathrm{cm}^{2}6.0 W/cm2
  4. D
    0.06 W/cm20.06\mathrm{~W} / \mathrm{cm}^{2}0.06 W/cm2
View written solutionFree

Correct answer: D

  1. Use radiation pressure-force relation for complete absorption

For light falling normally on a surface and being completely absorbed, the force is related to intensity by

F=IAcF = \frac{IA}{c}F=cIA​

where:

  • FFF = force,
  • III = energy flux (intensity),
  • AAA = area,
  • ccc = speed of light.

So,

I=FcAI = \frac{Fc}{A}I=AFc​

  1. Substitute the given values

Given:

  • F=7.2×10−9 NF = 7.2 \times 10^{-9}\ \text{N}F=7.2×10−9 N
  • A=36 cm2=36×10−4 m2=3.6×10−3 m2A = 36\ \text{cm}^2 = 36 \times 10^{-4}\ \text{m}^2 = 3.6 \times 10^{-3}\ \text{m}^2A=36 cm2=36×10−4 m2=3.6×10−3 m2
  • c=3×108 m/sc = 3 \times 10^8\ \text{m/s}c=3×108 m/s

Thus,

I=(7.2×10−9)(3×108)3.6×10−3I = \frac{(7.2 \times 10^{-9})(3 \times 10^8)}{3.6 \times 10^{-3}}I=3.6×10−3(7.2×10−9)(3×108)​

  1. Calculate numerator

7.2×10−9×3×108=21.6×10−1=2.167.2 \times 10^{-9} \times 3 \times 10^8 = 21.6 \times 10^{-1} = 2.167.2×10−9×3×108=21.6×10−1=2.16

So,

I=2.163.6×10−3I = \frac{2.16}{3.6 \times 10^{-3}}I=3.6×10−32.16​

  1. Calculate intensity

I=0.6×103=600 W/m2I = 0.6 \times 10^3 = 600\ \text{W/m}^2I=0.6×103=600 W/m2

  1. Convert to W/cm2\text{W/cm}^2W/cm2

Since

1 m2=104 cm21\ \text{m}^2 = 10^4\ \text{cm}^21 m2=104 cm2

therefore,

600 W/m2=600104 W/cm2=0.06 W/cm2600\ \text{W/m}^2 = \frac{600}{10^4}\ \text{W/cm}^2 = 0.06\ \text{W/cm}^2600 W/m2=104600​ W/cm2=0.06 W/cm2

  1. Match with options

0.06 W/cm20.06\ \text{W/cm}^20.06 W/cm2

So the correct option is D.

  1. Note about the given time

The time period of 20 minutes is not needed here, because the force given is already the average force. The radiation pressure relation directly gives intensity from force and area.

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