Electromagnetic Waves — Class 12 Physics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 12 Physics chapter "Electromagnetic Waves" — 8 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 12 Physics chapter "Electromagnetic Waves" — 8 important questions with detailed answers for CBSE board ex…

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Key Questions Covered:

What is an electromagnetic wave? Write its characteristics.
Derive the relationship between c, μ₀, and ε₀ for speed of electromagnetic wa…
What is meant by polarization of an electromagnetic wave? Describe linear and…
Light of intensity 0.50 W/m² is incident on a polarizer. What is the intensit…
State Brewster's law and derive the polarizing angle for reflected light.
An electromagnetic wave has electric field E = 50 sin(2π × 10⁷ t - 2π × 10⁻² …
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
What is an electromagnetic wave? Write its characteristics.	✓ Solved
Derive the relationship between c, μ₀, and ε₀ for speed o…	✓ Solved
What is meant by polarization of an electromagnetic wave?…	✓ Solved
Light of intensity 0.50 W/m² is incident on a polarizer. …	✓ Solved
State Brewster's law and derive the polarizing angle for …	✓ Solved
An electromagnetic wave has electric field E = 50 sin(2π …	✓ Solved

Showing 6 of 8 questions

Q1: What is an electromagnetic wave? Write its characteristics.

An electromagnetic wave is a transverse wave consisting of time-varying electric and magnetic fields perpendicular to each other and to the direction of propagation. Characteristics: 1. Transverse in nature — E and B oscillate perpendicular to direction of propagation 2. E and B are perpendicular to each other 3. Both E and B oscillate in phase 4. Speed in vacuum = c = 3 × 10⁸ m/s 5. Speed in medium = c/n where n is refractive index 6. Obey Maxwell's equations 7. Carry energy and momentum 8. Ca...

Q2: Derive the relationship between c, μ₀, and ε₀ for speed of electromagnetic waves.

From Maxwell's equations: ∇ × E = -dB/dt (Faraday's law) ∇ × B = μ₀ε₀(dE/dt) (Ampere-Maxwell law) For a plane wave traveling in +x direction: E = E₀ sin(kx - ωt) B = B₀ sin(kx - ωt) From Faraday's law: -dE/dx = dB/dt -E₀k cos(kx - ωt) = -B₀ω cos(kx - ωt) E₀k = B₀ω E₀/B₀ = ω/k = v From Ampere-Maxwell law: dB/dx = μ₀ε₀(dE/dt) B₀k cos(kx - ωt) = μ₀ε₀ E₀ω cos(kx - ωt) B₀k = μ₀ε₀ E₀ω Dividing first by second: (E₀/B₀)/(B₀k) = ω/(μ₀ε₀ E₀ω) 1/B₀² = μ₀ε₀/ω² ω/k = 1/√(μ₀ε₀) Therefore: c = 1/√(μ₀ε₀) ...

Q3: What is meant by polarization of an electromagnetic wave? Describe linear and circular polarization.

Polarization: Restriction of oscillation of electric field vector E to a particular direction perpendicular to propagation. Linear (plane) polarization: - E oscillates along a fixed direction (one plane) - E⃗ = E₀ sin(kx - ωt) ĵ (for oscillation in y-direction) - Can be obtained using polarizers (Nicol prism, polaroid) - Malus law: I = I₀ cos²θ (θ = angle between polarizer axes) Circular polarization: - E vector rotates in a plane perpendicular to propagation - E⃗ = E₀[sin(kx - ωt) ĵ + sin(kx ...

Q4: Light of intensity 0.50 W/m² is incident on a polarizer. What is the intensity of transmitted light? What if two polarizers are placed with axes at 60° to each other?

Case 1: Single polarizer Using Malus law: I = I₀ cos²θ For unpolarized light incident on first polarizer (θ = 0°): I₁ = I₀/2 = 0.50/2 = 0.25 W/m² Case 2: Two polarizers at 60° angle After first polarizer: I₁ = I₀/2 = 0.25 W/m² After second polarizer at 60° to first: I₂ = I₁ cos²(60°) = 0.25 × cos²(60°) cos(60°) = 0.5, so cos²(60°) = 0.25 I₂ = 0.25 × 0.25 = 0.0625 W/m² Alternatively: I₂ = (I₀/2) × cos²(60°) = (0.50/2) × 0.25 = 0.0625 W/m² Final answers: - Single polarizer: 0.25 W/m² - Two pola...

Q5: State Brewster's law and derive the polarizing angle for reflected light.

Brewster's Law: When unpolarized light is incident at a particular angle (Brewster's angle), the reflected light is completely polarized with E parallel to the surface. Derivation: At Brewster's angle θ_B: - Reflected ray is perpendicular to refracted ray - θ_B + θ_r = 90° where θ_r is refraction angle From Snell's law: sin θ_B = n sin θ_r Since θ_r = 90° - θ_B: sin θ_B = n sin(90° - θ_B) sin θ_B = n cos θ_B tan θ_B = n Bruesterer's Angle: θ_B = tan⁻¹(n) or θ_B = tan⁻¹(n₂/n₁) For air-glass ...

Q6: An electromagnetic wave has electric field E = 50 sin(2π × 10⁷ t - 2π × 10⁻² x) V/m in SI units. Find wavelength, frequency, and period.

Given: E = 50 sin(2π × 10⁷ t - 2π × 10⁻² x) V/m Comparing with standard form: E = E₀ sin(ωt - kx) E₀ = 50 V/m ω = 2π × 10⁷ rad/s k = 2π × 10⁻² rad/m Frequency: ω = 2πν ν = ω/(2π) = (2π × 10⁷)/(2π) = 10⁷ Hz = 10 MHz Wavelength: k = 2π/λ λ = 2π/k = 2π/(2π × 10⁻²) = 1/(10⁻²) = 100 m Period: T = 1/ν = 1/(10⁷) = 10⁻⁷ s = 0.1 μs Verification: v = νλ = 10⁷ × 100 = 10⁹ m/s (Note: This is > c, so this may be internal wave or error in problem. If v = c, then ν ≈ 3 × 10⁶ Hz) Answers: - Wavelength:...

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