Radiation Pressure
A perfectly absorbing solar sail receives light of energy \cup from the Sun over a given interval, and an engineer computes the momentum transferred to it.
Select the correct option:
Solution
U/c
As NCERT Class 12, Chapter 8 (Electromagnetic Waves) explains, electromagnetic waves carry not only energy but also linear momentum, a direct consequence of Maxwell's equations. For a wave delivering energy \cup to a surface that completely absorbs it, the momentum transferred is p = U/c, where c is the speed of light. When the surface absorbs the radiation, it also absorbs all the momentum the wave carried, and by Newton's second law this rate of momentum transfer manifests as a force, giving rise to radiation pressure. This is why sunlight exerts a small but real pressure, which can propel a solar sail over long periods even though the effect is minute per second. The option U·c is dimensionally incorrect since multiplying energy by speed does not give momentum. The option U/c² corresponds to a mass-like quantity from E = mc² rather than the momentum of radiation, so it is wrong. The option 2U/c applies to a perfectly reflecting surface, where the momentum change is doubled because the light reverses direction; for a purely absorbing sail the factor of two does not apply. A dimensional check shows that energy (J) divided by speed (m/s) gives kg·m/s, the correct unit of momentum, confirming that U/c is the right expression for an absorbing surface.
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About This Question
- Subject
- physics
- Chapter
- electromagnetic waves
- Topic
- radiation pressure
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
U/c
As NCERT Class 12, Chapter 8 (Electromagnetic Waves) explains, electromagnetic waves carry not only energy but also linear momentum, a direct consequence of Maxwell's equations. For a wave delivering energy \cup to a surface that completely absorbs it, the momentum transferred is p = U/c, where c is the speed of light. When the surface absorbs the radiation, it also absorbs all the momentum the wave carried, and by Newton's second law this rate of momentum transfer manifests as a force, giving rise to radiation pressure. This is why sunlight exerts a small but real pressure, which can propel a solar sail over long periods even though the effect is minute per second. The option U·c is dimensionally incorrect since multiplying energy by speed does not give momentum. The option U/c² corresponds to a mass-like quantity from E = mc² rather than the momentum of radiation, so it is wrong. The option 2U/c applies to a perfectly reflecting surface, where the momentum change is doubled because the light reverses direction; for a purely absorbing sail the factor of two does not apply. A dimensional check shows that energy (J) divided by speed (m/s) gives kg·m/s, the correct unit of momentum, confirming that U/c is the right expression for an absorbing surface.
This hard difficulty physics question is from the chapter electromagnetic waves, covering the topic of radiation pressure. It appeared in the 2025 exam.
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