Electromagnetic Waves — Previous Year Questions (Class 12 Physics)
Electromagnetic waves are oscillating electric and magnetic fields. Master Maxwell's equations, wave properties, and the EM spectrum.
TL;DR: Electromagnetic waves are oscillating electric and magnetic fields. Master Maxwell's equations, wave properties, and the EM spectrum.
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Electromagnetic waves are oscillating electric and magnetic fields. Master Maxwell's equations, wave properties, and the EM spectrum.
Electromagnetic Waves — Previous Year Questions with Solutions
Q (2023, 3 marks): Define an electromagnetic wave and explain how electric and magnetic fields are related in it.
Answer: An electromagnetic wave is a propagating disturbance consisting of time-varying electric and magnetic fields perpendicular to each other and to the direction of propagation.
Characteristics:
1. Electric field E and magnetic field B are perpendicular to each other
2. Both E and B are perpendicular to the direction of propagation
3. E and B oscillate in phase (zero and maximum simultaneously)
4. The ratio of magnitudes: E/B = c (speed of light)
5. Energy is equally distributed between electric and magnetic fields
Mathematical representation:
E = E₀ sin(kx - ωt) and B = B₀ sin(kx - ωt)
where E₀/B₀ = c
Relation: E = cB (at any instant)
Final Answer: EM wave has perpendicular E and B fields oscillating in phase with E = cB relation
Q (2022, 2 marks): Calculate the wavelength of electromagnetic radiation with frequency 5 × 10¹⁴ Hz. (c = 3 × 10⁸ m/s)
Answer: Using c = fλ
λ = c/f = (3 × 10⁸)/(5 × 10¹⁴)
λ = (3/5) × 10⁻⁶
λ = 0.6 × 10⁻⁶ = 6 × 10⁻⁷ m = 600 nm
This wavelength corresponds to red light in the visible spectrum.
Final Answer: λ = 6 × 10⁻⁷ m or 600 nm
Q (2023, 5 marks): The equation of an electromagnetic wave is E = 50 cos(2π × 10⁶ t - 2π x/1000) V/m. Find (i) amplitude, (ii) wavelength, (iii) frequency, (iv) wave speed.
Answer: Standard form: E = E₀ cos(ωt - kx)
Given: E = 50 cos(2π × 10⁶ t - 2π x/1000)
Comparing: E₀ = 50 V/m, ω = 2π × 10⁶, k = 2π/1000
(i) Amplitude: E₀ = 50 V/m
(ii) Wavelength: λ = 2π/k = 2π/(2π/1000) = 1000 m
(iii) Frequency: f = ω/(2π) = (2π × 10⁶)/(2π) = 10⁶ Hz = 1 MHz
(iv) Wave speed: v = ω/k = (2π × 10⁶)/(2π/1000) = 10⁶ × 1000 = 10⁹ m/s
Note: This is faster than light, so it's not a real EM wave. Likely an error in the problem.
If we assume it should be E = 50 cos(2π × 10⁶ t - 2π × 10⁶ x / (3×10⁸)):
Then v = c = 3 × 10⁸ m/s (physical).
Final Answer: (i) E₀ = 50 V/m, (ii) λ = 1000 m, (iii) f = 10⁶ Hz, (iv) v = 10⁹ m/s (note: unphysical)
Q (2021, 5 marks): State Maxwell's equations and their physical significance.
Answer: Maxwell's Four Equations:
1. Gauss's Law (Electric): ∮ E·dA = Q/ε₀
Physical meaning: Electric field originates from electric charges. Total electric flux through a closed surface equals the enclosed charge divided by ε₀.
2. Gauss's Law (Magnetic): ∮ B·dA = 0
Physical meaning: Magnetic monopoles don't exist. Magnetic field lines are always closed loops.
3. Faraday's Law: ∮ E·dl = -dΦ_B/dt
Physical meaning: A changing magnetic field induces an electric field. This is the basis of electromagnetic induction.
4. Ampère-Maxwell Law: ∮ B·dl = μ₀(I_enc + ε₀ dΦ_E/dt)
Physical meaning: An electric current produces a magnetic field. A changing electric field also produces a magnetic field.
Significance: These four equations unify electricity, magnetism, and optics. They predict electromagnetic waves traveling at speed c = 1/√(μ₀ε₀), explaining the nature of light.
Final Answer: Four Maxwell equations unified electricity and magnetism; predict EM waves with c = 1/√(μ₀ε₀)
Q (2022, 2 marks): Arrange the following EM radiations in increasing order of wavelength: ultraviolet, visible light, infrared, radio waves, X-rays.
Answer: EM spectrum in order of increasing wavelength (decreasing frequency):
X-rays < Ultraviolet < Visible light < Infrared < Radio waves
Approximate wavelength ranges:
X-rays: 10⁻¹¹ - 10⁻⁸ m
Ultraviolet: 10⁻⁸ - 4 × 10⁻⁷ m
Visible light: 4 × 10⁻⁷ - 7 × 10⁻⁷ m
Infrared: 7 × 10⁻⁷ - 10⁻³ m
Radio waves: 10⁻³ - 10⁴ m
Final Answer: X-rays < UV < Visible < IR < Radio waves
Q (2023, 3 marks): Calculate the energy of a photon with wavelength 600 nm. (h = 6.63 × 10⁻³⁴ J·s, c = 3 × 10⁸ m/s)
Answer: Wavelength λ = 600 nm = 600 × 10⁻⁹ m = 6 × 10⁻⁷ m
Frequency: f = c/λ = (3 × 10⁸)/(6 × 10⁻⁷) = 0.5 × 10¹⁵ = 5 × 10¹⁴ Hz
Energy of photon: E = hf = (6.63 × 10⁻³⁴)(5 × 10¹⁴)
E = 33.15 × 10⁻²⁰ = 3.315 × 10⁻¹⁹ J
Alternatively: E = hc/λ = (6.63 × 10⁻³⁴ × 3 × 10⁸)/(6 × 10⁻⁷)
E = (6.63 × 3 × 10⁻²⁶)/(6 × 10⁻⁷) = (19.89 × 10⁻²⁶)/(6 × 10⁻⁷)
E = 3.315 × 10⁻¹⁹ J ≈ 3.3 × 10⁻¹⁹ J
Final Answer: E ≈ 3.3 × 10⁻¹⁹ J
Frequently Asked Questions
Why is light considered an electromagnetic wave?
Light is electromagnetic radiation in the visible range (400-700 nm). Maxwell's equations predict that oscillating electric and magnetic fields propagate as waves at speed c = 1/√(μ₀ε₀). Experiments like double-slit interference and Young's experiment confirm light's wave nature. Electromagnetic waves don't require a medium and can travel through vacuum, unlike mechanical waves.
What is the relationship between wavelength, frequency, and speed of an electromagnetic wave?
For all EM waves: c = fλ, where c is speed of light (3 × 10⁸ m/s), f is frequency, and λ is wavelength. This shows that wavelength and frequency are inversely proportional for EM waves. Longer wavelengths correspond to lower frequencies (e.g., radio waves), while shorter wavelengths correspond to higher frequencies (e.g., X-rays).
More Class 12 Physics PYQs
- Current Electricity
- Ray Optics
- Electrostatics
- Moving Charges and Magnetism
- Electromagnetic Induction
- Alternating Current
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