Energy, momentum, and radiation pressure of electromagnetic waves
Electromagnetic waves transport energy and momentum, exerting radiation pressure and force on surfaces, with quantifiable energy density and intensity.
Why this shows up in the exam
NEET includes questions on how electromagnetic waves interact with matter and how to calculate related physical quantities.
How NEET tests this
Learn the idea
Electromagnetic waves carry energy and momentum; when they strike a surface they exert a radiation pressure that produces a force.
🧠 Memory hook: I‑c‑P‑2P (Intensity → c → Pressure, double for perfect reflector)
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Intensity I is the energy flux (energy per unit area per unit time) of the wave
- Radiation pressure on a perfectly absorbing surface is I/c and on a perfectly reflecting surface is 2I/c
- Momentum associated with radiation of energy E is E/c
- Electric and magnetic fields store equal energy, so their contributions to intensity are in the ratio 1:1
- Force on a surface equals radiation pressure multiplied by the illuminated area
How to approach it
- 1Identify the required quantity and the nature of the surface (absorbing or reflecting)
- 2Write the NCERT relation appropriate to that situation (P=I/c or P=2I/c, p=E/c, F=P·A)
- 3Insert the given numbers, keep units consistent, and compute the answer
Worked example — watch it click
Light with an energy flux of 25 × 10⁴ W m⁻² falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm², the average force exerted on the surface is:
- A)1.20 × 10⁻⁶ N
- B)3.0 × 10⁻⁶ N
- C)1.25 x 10⁻⁶ N
- ✅2.50 × 10⁻⁶ N
The concept behind this problem
The example forces you to apply the NCERT formula P=2I/c for a reflecting surface and then use F=P·A, directly testing the idea that EM waves transfer momentum and exert pressure.
Step by step
- 1Energy flux (intensity) I = 25×10⁴ W/m², Area A = 15 cm² = 15×10⁻⁴ m².
- 2For perfect reflection at normal incidence, radiation pressure P = 2I/c.
- 3Force F = P×A = (2I/c)×A = (2×25×10⁴×15×10⁻⁴)/(3×10⁸) = (2×25×15×10⁰)/(3×10⁸) = 750/(3×10⁸) = 2.5×10⁻⁶ N.
Watch out
Using I/c instead of 2I/c for a reflecting surface cuts the force in half.
Common slip-ups that cost marks
- •Missing the factor of two for a perfectly reflecting surface
- •Confusing intensity with energy density; intensity is power per unit area, not stored energy
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
Light with an energy flux of 25 × 10⁴ W m⁻² falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm², the average force exerted on the surface is:
Push further
More challenging13 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.
An electromagnetic wave propagates through a vacuum. If the average energy density due to its electric field is 2.0 x 10⁻⁸ J/m³, what is the average energy density due to its magnetic field?
More from Electromagnetic Waves
Mathematical relations in electromagnetic waves
Key mathematical relationships in electromagnetic waves include the connection between electric and magnetic field amplitudes, wave speed, wavelength, frequency, and the wave equation parameters.
Nature and properties of electromagnetic waves
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Production and propagation of electromagnetic waves
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Electromagnetic spectrum
The electromagnetic spectrum encompasses all types of electromagnetic waves, classified by wavelength or frequency, with each region having characteristic properties and applications.
How Electromagnetic Waves Are Produced
Electromagnetic radiation is generated by accelerated charges or time-varying currents. In a source-free region, coupled time-varying electric and magnetic fields propagate without requiring a material medium.
Maxwell Equations as a Unified Picture
The integral Maxwell equations are Gauss's electric law, Gauss's magnetic law, Faraday's induction law, and the Ampere-Maxwell law. Together in a charge-free, current-free region they imply electromagnetic wave equations.