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This MCQ module is based on: Em Waves Properties
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Em Waves Properties
🎓 Class 12
Physics
CBSE
Theory
Ch 8 – Electromagnetic Waves
⏱ ~14 min
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Em Waves Properties
8.4 Electromagnetic Waves — Their Nature
From Maxwell's equations one can derive a wave equation that has plane-wave solutions of the form:
\(E_y(x,t) = E_0\sin(kx - \omega t),\quad B_z(x,t) = B_0\sin(kx - \omega t)\)
Here the wave propagates along +x; the electric field oscillates along y; the magnetic field oscillates along z. Three crucial features fall out:
- Transverse: Both E and B are perpendicular to the direction of propagation \(\hat{c}\).
- E ⊥ B: The electric field is perpendicular to the magnetic field at every instant.
- In phase: E and B reach their maxima and zeros at the same instants.
Furthermore the amplitudes are related by:
\(\boxed{\dfrac{E_0}{B_0} = c = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}}}\)
8.5 Sources of EM Waves — Hertz's Experiment
Maxwell predicted EM waves theoretically in 1865. The decisive experimental confirmation came two decades later when Heinrich Hertz built a spark-gap transmitter and a loop receiver (1887).
8.5.1 Hertz Apparatus
- Transmitter: a high-voltage induction coil charges two metal balls separated by a small spark gap. When the breakdown voltage is reached the spark jumps, driving rapid oscillation of charge in the connected wire dipole — radiating EM waves at ~50 MHz.
- Receiver: a separate copper-wire loop with its own tiny spark gap, placed across the room. Tiny sparks appear in this gap whenever the transmitter sparks — proof that the radiation has crossed the room.
8.5.2 Hertz's Conclusions
- The radiation could be reflected by metal sheets and refracted by a pitch prism - just like light.
- It could be polarised by passing through a wire grid.
- Its measured speed equalled c - confirming Maxwell's prediction.
An accelerating (or decelerating) charge is the fundamental source of EM waves. Stationary or uniformly moving charges produce only static fields - no radiation.
8.6 Speed of Electromagnetic Waves
Maxwell's equations applied to a plane wave in vacuum yield the wave speed:
\(c = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}} = \dfrac{1}{\sqrt{(4\pi\times10^{-7})(8.854\times10^{-12})}} = 2.998 \times 10^8 \text{ m/s}\)
In a material medium of permittivity ε and permeability μ:
\(v = \dfrac{1}{\sqrt{\mu\varepsilon}},\quad n = \dfrac{c}{v} = \sqrt{\dfrac{\mu\varepsilon}{\mu_0\varepsilon_0}} = \sqrt{\varepsilon_r \mu_r}\)
For most non-magnetic transparent media \(\mu_r \approx 1\), giving the familiar \(n \approx \sqrt{\varepsilon_r}\).
| Quantity | Symbol | Value (SI) | Comment |
|---|---|---|---|
| Permittivity of free space | ε₀ | 8.854 × 10⁻¹² F/m | describes E in vacuum |
| Permeability of free space | μ₀ | 4π × 10⁻⁷ T·m/A | describes B in vacuum |
| Speed of light in vacuum | c | 2.998 × 10⁸ m/s | = 1/√(μ₀ε₀) |
| Speed in medium | v | c/n | n = refractive index |
| Ratio E₀ / B₀ | — | c | in vacuum |
8.6.1 The Wave Relations
All sinusoidal waves obey \(c = f\lambda\). For EM waves additionally:
\(\omega = ck,\qquad k = \dfrac{2\pi}{\lambda},\qquad T = \dfrac{1}{f}\)
Example 8.3 — Wavelength of a microwave
A microwave oven operates at 2.45 GHz. Find (a) wavelength in vacuum, (b) wave number k.
(a) λ = c/f = (3 × 10⁸)/(2.45 × 10⁹) = 0.122 m = 12.2 cm. (This explains why microwave ovens are about 30 cm wide - to accommodate several half-wavelengths for a standing-wave pattern that heats food more evenly.)
(b) k = 2π/λ = 51.5 rad/m.
Example 8.4 — Amplitude relations
An EM wave in vacuum has peak electric field E0 = 50 N/C. Find (a) peak magnetic field B0, (b) peak energy density of the E-field, (c) peak energy density of the B-field.
(a) B0 = E0/c = 50/(3 × 10⁸) = 1.67 × 10⁻⁷ T.
(b) uEmax = ½ ε₀ E₀² = ½ × 8.854×10⁻¹² × 2500 = 1.11 × 10⁻⁸ J/m³.
(c) uBmax = B₀²/(2μ₀) = (1.67×10⁻⁷)²/(8π×10⁻⁷) = 1.11 × 10⁻⁸ J/m³.
The two peak energy densities are equal - a basic feature of an EM wave: energy is shared equally between E and B.
Simulation: EM Wave Calculator (E, B and c)
Set the frequency. Read the wavelength, wave number, period and the E-to-B ratio (always c).
| Wavelength λ | 12.2 cm |
| Wave number k | 51.5 rad/m |
| Period T | 0.408 ns |
| Peak magnetic field B₀ | 1.67×10⁻⁷ T |
| Speed c (in vacuum) | 2.998 × 10⁸ m/s (always) |
Activity 8.2 — Light is an EM wave (polarisation)
Pick up two polarising filters (sunglasses lenses or photography filters).
Predict: how will the transmitted light change as you slowly rotate one filter relative to the other?
- Hold them stacked, lined up, looking at a lamp.
- Slowly rotate one filter through 90°.
Light brightness falls as you rotate. At 90° the field is almost completely blocked (Malus's law: I = I₀ cos²θ). This is possible only because light is a TRANSVERSE wave - the E-field oscillates perpendicular to propagation, so a polariser can let through only one polarisation component. Longitudinal waves (sound) cannot be polarised.
Competency-Based Questions L1L2L3L4L5
A radio station transmits at 102.6 MHz. The peak electric field at a receiver is 1.2 × 10⁻³ V/m.
1. The wavelength of the broadcast is closest to: L1
(b) 2.9 m. λ = c/f = 3×10⁸/(102.6×10⁶) = 2.92 m.
2. Explain why E and B in an EM wave are in phase. L2
Both fields satisfy the same wave equation with the same speed c. Plane-wave solutions of the form sin(kx − ωt) have a common time-dependent factor — peaks, zeros and minima of E and B coincide in time and space.
3. Find the peak magnetic field at the receiver. L3
B₀ = E₀/c = (1.2×10⁻³)/(3×10⁸) = 4 × 10⁻¹² T.
4. Justify Hertz's claim that EM waves are transverse using one of his observations. L4
Hertz showed that placing a wire-grid polariser in front of the receiver loop blocked the radiation when the grid was rotated by 90°. Only transverse waves can be polarised (the E-field oscillation has a direction perpendicular to propagation). Longitudinal waves cannot be polarised.
5. Critique the statement: "Static charges and uniformly moving charges both produce EM waves." L5
FALSE. A static charge produces only a static E-field (no B). A uniformly moving charge produces a static E-field plus a steady B-field (in the lab frame) but no time-varying fields ⇒ no radiation. Only ACCELERATED charges radiate EM waves.
Assertion-Reason Questions
Assertion: The ratio E₀/B₀ for an EM wave in vacuum equals the speed of light.
Reason: Maxwell's equations require E and B amplitudes to be related by c = 1/√(μ₀ε₀).
(A). Both true; R explains A.
Assertion: EM waves cannot travel through a perfect vacuum.
Reason: Waves require a material medium to vibrate.
(D). A is false (EM waves travel best in vacuum - they reach us from the Sun). R is true only of mechanical waves.
Assertion: In an EM wave the energy is shared equally between the electric and magnetic fields.
Reason: The energy densities are uE = ½ ε₀E² and uB = B²/(2μ₀), and with E = cB these become equal.
(A). Both true; R explains A.
Frequently Asked Questions - Em Waves Properties
What is the main concept covered in Em Waves Properties?
In NCERT Class 12 Physics Chapter 8 (Electromagnetic Waves), "Em Waves Properties" 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 Em Waves Properties useful in real-life applications?
Real-life applications of "Em Waves Properties" 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 Em Waves Properties?
Key formulas in "Em Waves Properties" (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. "Em Waves Properties" 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 Em Waves Properties?
CBSE board questions from "Em Waves Properties" 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 "Em Waves Properties" 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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