JEE Advanced 2026 Paper 2 — Full Mock Test (54 Questions, 180 Marks)
Mathematics · Physics · Chemistry
This MCQ module is based on: Energy Momentum Applications
TOPIC 37 OF 38
Energy Momentum Applications
🎓 Class 12
Physics
CBSE
Theory
Ch 8 – Electromagnetic Waves
⏱ ~14 min
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Energy Momentum Applications
8.8 Energy Carried by an EM Wave
An EM wave transports energy through the oscillating E and B fields. The energy density at any instant is the sum of contributions from E and B:
\(u = u_E + u_B = \dfrac{1}{2}\varepsilon_0 E^2 + \dfrac{B^2}{2\mu_0}\)
Substituting B = E/c and using c² = 1/(μ₀ε₀):
\(u_B = \dfrac{B^2}{2\mu_0} = \dfrac{E^2/c^2}{2\mu_0} = \dfrac{\varepsilon_0 E^2}{2} = u_E\)
The electric and magnetic contributions are equal at every instant. Therefore:
\(u = \varepsilon_0 E^2 = \dfrac{B^2}{\mu_0}\)
Averaging over one cycle (using \(\langle\sin^2\rangle = 1/2\)):
\(\langle u\rangle = \dfrac{1}{2}\varepsilon_0 E_0^2 = \dfrac{B_0^2}{2\mu_0}\)
8.8.1 Intensity (Poynting Vector)
The energy crossing unit area per unit time is the intensity I:
\(I = c\,\langle u\rangle = \dfrac{1}{2}c\varepsilon_0 E_0^2 = \dfrac{c B_0^2}{2\mu_0}\)
In vector form the energy flux density is the Poynting vector \(\vec{S} = (1/\mu_0)\vec{E}\times\vec{B}\); its magnitude time-averaged equals I.
8.9 Momentum and Radiation Pressure
A travelling EM wave carries linear momentum as well as energy. If a beam of total energy U is absorbed completely by a surface, it deposits momentum:
\(p = \dfrac{U}{c}\)
Radiation Pressure: The pressure exerted by an EM wave on a surface:
- Perfect absorber: \(P_{rad} = I/c\)
- Perfect reflector: \(P_{rad} = 2I/c\) (momentum is reversed, change is twice as large)
| Quantity | Formula (peak) | Formula (avg) | SI Unit |
|---|---|---|---|
| Electric energy density | uE = ½ε₀E² | ¼ε₀E₀² | J/m³ |
| Magnetic energy density | uB = B²/(2μ₀) | B₀²/(4μ₀) | J/m³ |
| Total energy density | u = ε₀E² | ½ε₀E₀² | J/m³ |
| Intensity | — | I = ½cε₀E₀² = cB₀²/(2μ₀) | W/m² |
| Momentum (absorbed) | — | p = U/c | kg·m/s |
| Radiation pressure (absorbed) | — | I/c | Pa |
| Radiation pressure (reflected) | — | 2I/c | Pa |
8.10 Applications of EM Waves
- Communication - AM, FM radio; TV, mobile phone networks, Wi-Fi, Bluetooth use radio and microwaves; optical fibres carry IR for high-speed data.
- Cooking - microwave ovens.
- Remote sensing - IR satellites for crop and weather monitoring; radar (microwaves) for aircraft and weather.
- Medical - X-ray radiography, CT, gamma-knife oncology, IR thermography, UV sterilisation, MRI (radio-frequency).
- Security - X-ray baggage scanners, millimetre-wave body scanners.
- Astronomy - radio telescopes, IR (JWST), visible, UV, X-ray and γ-ray telescopes each open a window onto different cosmic processes.
- Industrial - IR heating, UV curing of inks, X-ray non-destructive testing.
- Solar power - photovoltaic cells convert visible/IR to electricity; solar thermal plants concentrate sunlight to heat water.
Health note: Ionising EM radiation (UV-C, X, γ) can damage DNA and cause cancer. Always use shielding when handling these sources - the dose absorbed (sievert, Sv) must stay below regulatory limits.
Example 8.8 — Intensity at the Earth
At the surface of the Earth the average solar intensity is 1.4 kW/m². Find (a) peak electric field, (b) peak magnetic field, (c) radiation pressure on a black absorbing surface.
(a) I = ½ c ε₀ E₀² ⇒ E₀ = √(2I/(cε₀)) = √(2×1400/(3×10⁸ × 8.854×10⁻¹²)) = √(1054) = 1027 V/m ≈ 1.03 kV/m.
(b) B₀ = E₀/c = 1027/3×10⁸ = 3.42 × 10⁻⁶ T.
(c) Prad = I/c = 1400/3×10⁸ = 4.67 × 10⁻⁶ Pa.
Example 8.9 — Light pressure on a mirror
A laser beam delivers 5 W of power on a 1 cm² spot on a perfectly reflecting mirror. Find the radiation pressure.
Intensity I = 5 / 10⁻⁴ = 5 × 10⁴ W/m².
For a perfect reflector: P = 2I/c = (2 × 5×10⁴)/(3×10⁸) = 3.33 × 10⁻⁴ Pa.
Tiny pressure - but in a vacuum, integrated over years, drives solar-sail spacecraft.
Example 8.10 — Photon momentum
How much momentum does a 1 J pulse of light carry?
p = U/c = 1/3×10⁸ = 3.33 × 10⁻⁹ kg·m/s.
Simulation: Intensity, Energy Density & Radiation Pressure
Set the peak electric field E₀. The simulator returns the energy density, intensity and radiation pressure (both absorbed and reflected).
| Peak B-field B₀ | 3.42 μT |
| Avg energy density <u> | 4.67 × 10⁻⁶ J/m³ |
| Intensity I | 1400 W/m² |
| Radiation pressure (absorbed) | 4.67 μPa |
| Radiation pressure (reflected) | 9.34 μPa |
Activity 8.4 — Crookes radiometer (light mill)
A Crookes radiometer is a glass bulb at low pressure containing four vanes, black on one side, silvered on the other, mounted on a spindle.
Predict: when sunlight falls on it, which way will the vanes rotate?
The vanes spin with the silvered side moving forward and the black side trailing. Counter-intuitively the cause is NOT radiation pressure (which would push the silvered side back) but residual gas in the bulb: gas molecules near the warmer black face leave with more energy than they arrive, kicking the vane forward. Pure radiation pressure can be demonstrated only at much higher vacuum, as in the Nichols radiometer (1901).
Competency-Based Questions L1L2L3L4L6
A 100 W incandescent bulb radiates uniformly in all directions. A small light sensor of area 1 cm² is placed 2 m away.
1. Intensity at the sensor location is closest to: L1
(b) 2 W/m². I = P/(4πr²) = 100/(4π × 4) ≈ 1.99 W/m².
2. Define energy density of an EM wave and write its formula. L1
Energy density = energy stored per unit volume. For an EM wave: u = ½ε₀E² + B²/(2μ₀) = ε₀E². Average: ⟨u⟩ = ½ε₀E₀².
3. Find the peak E-field at the sensor. L3
E₀ = √(2I/(cε₀)) = √(2 × 1.99/(3×10⁸ × 8.854×10⁻¹²)) = √(1499) ≈ 38.7 V/m.
4. The sensor surface is now made perfectly reflecting. Compare the force on it before and after. L4
Before (perfect absorber): F = IA/c = 1.99 × 10⁻⁴/3×10⁸ = 6.6 × 10⁻¹³ N. After (perfect reflector): F = 2IA/c = 1.3 × 10⁻¹² N - exactly DOUBLE. Reason: reflection reverses the photon momentum, so the change is twice as large.
5. Propose an experiment that could detect radiation pressure of light without confounding gas-pressure effects. L6
Use a high-vacuum chamber (P < 10⁻⁶ Pa) with a torsion balance carrying a mirror. Direct a chopped intense laser on the mirror and synchronise the torsion-balance deflection with the chopper frequency (lock-in detection) to subtract any residual thermal noise. This is the Nichols radiometer technique - first successful in 1901.
Assertion-Reason Questions
Assertion: A perfectly reflecting surface experiences twice the radiation pressure of a perfectly absorbing surface for the same beam.
Reason: Reflection reverses the photon momentum so the change in momentum is doubled.
(A). Both true; R explains A.
Assertion: The intensity of sunlight at Pluto is much less than at the Earth.
Reason: Intensity follows an inverse-square law I ∝ 1/r² for an isotropic source.
(A). Both true; R explains A. Pluto is ~40 AU from the Sun, so I is ~1/1600 of Earth's.
Assertion: A 100 J light pulse carries momentum 3.3 × 10⁻⁷ kg·m/s.
Reason: Momentum of a light pulse equals U/c where U is the energy and c the speed of light.
(A). Both true; R explains A. p = 100/(3×10⁸) = 3.3 × 10⁻⁷ kg·m/s.
Frequently Asked Questions - Energy Momentum Applications
What is the main concept covered in Energy Momentum Applications?
In NCERT Class 12 Physics Chapter 8 (Electromagnetic Waves), "Energy Momentum Applications" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Energy Momentum Applications useful in real-life applications?
Real-life applications of "Energy Momentum Applications" from NCERT Class 12 Physics Chapter 8 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Energy Momentum Applications?
Key formulas in "Energy Momentum Applications" (NCERT Class 12 Physics Chapter 8 Electromagnetic Waves) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 8?
NCERT Class 12 Physics Chapter 8 (Electromagnetic Waves) is structured so each part builds on the previous one. "Energy Momentum Applications" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Energy Momentum Applications?
CBSE board questions from "Energy Momentum Applications" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Energy Momentum Applications" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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