Chapter summary — Electromagnetic Waves
Electromagnetic (EM) waves are transverse waves of electric and magnetic fields that propagate through space at the speed of light c. Maxwell's equations predict EM waves and relate E and B fields; key relation in vacuum: c = 1/√(μ0ε0). EM spectrum ranges from radio waves, microwaves, infrared, visible, ultraviolet, X-rays to gamma rays. Important concepts: wave equation, Poynting vector S = (1/μ0)(E × B) (energy flux), intensity and energy density (u = ε0 E^2 = B^2/μ0), polarization (linear, circular, elliptical), reflection/refraction, boundary conditions, electromagnetic waves in media (refractive index n), dispersion, group and phase velocity, antennas and applications. Remember Maxwell-Faraday and Maxwell-Ampère corrections (displacement current) for completeness.
Revision tips: Memorize c = 3×10^8 m/s, relation c = fλ, Poynting vector direction, transverse nature (E ⟂ B ⟂ k), polarization rules and basic spectrum wavelengths. Practice simple wave problems and boundary condition applications.
1. Electromagnetic waves in vacuum are:
A) Transverse waves (E and B perpendicular to direction of propagation) ✅
B) Longitudinal waves
C) Surface waves
D) Pressure waves
2. Speed of electromagnetic waves in vacuum c is given by:
A) 1/√(μ0ε0) ✅
B) μ0ε0
C) √(μ0ε0)
D) μ0/ε0
3. The Poynting vector S represents:
A) Energy flux (power per unit area) of EM wave ✅
B) Electric potential
C) Magnetic field only
D) Charge density
4. For an electromagnetic wave in vacuum, the ratio E/B equals:
A) c (speed of light) ✅
B) 1/c
C) μ0
D) ε0
5. Relation between frequency f, wavelength λ and speed c is:
A) c = fλ ✅
B) c = f/λ
C) c = λ/f
D) c = f + λ
6. Which Maxwell's equation introduces displacement current term?
A) Gauss's law
B) Ampère's circuital law (Maxwell-Ampère law) ✅
C) Faraday's law
D) Gauss's law for magnetism
7. Electromagnetic waves are generated by:
A) Accelerated charges (time-varying currents) ✅
B) Static charges
C) Constant current
D) Magnetic monopoles
8. The energy density u of an electromagnetic wave in free space is proportional to:
A) E^2 (electric field squared) ✅
B) E
C) B
D) 1/E
9. Polarization of light refers to:
A) Orientation of the electric field vector ✅
B) Direction of propagation
C) Frequency only
D) Intensity only
10. Which part of EM spectrum has highest energy photons?
A) Gamma rays ✅
B) Radio waves
C) Microwaves
D) Infrared
11. In a plane electromagnetic wave, E, B and direction of propagation k are related as:
A) E ⟂ B ⟂ k (mutually perpendicular) ✅
B) E ∥ B
C) E ∥ k
D) B ∥ k
12. The intensity I of an EM wave is proportional to:
A) Average value of the Poynting vector (⟨S⟩) ✅
B) Frequency only
C}">C) Wavelength only
D) Charge density
13. When light passes from air into glass, its frequency and wavelength do what respectively?
A) Frequency remains same; wavelength decreases ✅
B) Frequency decreases; wavelength same
C}">C) Both increase
D) Frequency increases; wavelength increases
14. Dispersion in a medium refers to:
A) Variation of refractive index with frequency ⇒ different speeds for different λ ✅
B) Absorption only
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D) Reflection
15. The phenomenon where EM wave changes direction at boundary between media is:
A) Diffraction
B) Refraction ✅
C) Polarization
D) Interference
16. Brewster's angle corresponds to:
A) Angle where reflected light is fully polarized ✅
B) Angle of total internal reflection
C) Angle of incidence = 0
D) None
17. A linearly polarized wave can be converted to circularly polarized using:
A) Quarter-wave plate ✅
B) Polarizer only
C) Grating
D) Lens
18. Skin depth δ in a good conductor for EM waves varies with frequency as:
A) δ ∝ 1/√ω ✅
B) δ ∝ ω
C) δ ∝ 1/ω
D) δ independent of ω
19. Poynting vector S points in the direction of:
A) Energy flow and wave propagation ✅
B) Magnetic field only
C) Electric field only
D) None
20. Which equation describes time-varying electric and magnetic fields producing EM waves?
A) Maxwell's equations (with displacement current) ✅
B) Newton's laws
C) Schrödinger equation
D) Bernoulli's equation
21. Radio waves have _____ frequency and _____ wavelength compared to visible light.
A) Lower frequency; longer wavelength ✅
B) Higher frequency; shorter wavelength
C) Same frequency; same wavelength
D) Higher frequency; longer wavelength
22. The electric field of a plane EM wave can be written as E = E_0 cos(kx − ωt). The corresponding magnetic field B is:
A) B = (E_0/c) cos(kx − ωt) in perpendicular direction ✅
B) B = E_0 cos(kx − ωt) same direction
C) B = 0
D) B = (c/E_0) cos(kx − ωt)
23. Electromagnetic waves do not require a medium because:
A) They are self-sustaining oscillations of E and B fields ✅
B) They use air by default
C) They travel on wires only
D) They are sound waves
24. Which phenomenon causes separation of different frequencies of white light by a prism?
A) Interference
B) Dispersion due to varying refractive index with λ ✅
C) Polarization
D) Reflection
25. In vacuum, energy density u of EM wave is equally divided between electric and magnetic fields. So u = ε0 E^2 = B^2/μ0. The total energy density equals:
A) ε0 E^2 + B^2/μ0 ✅
B) ε0 E
C) B^2
D) 0
26. Blackbody radiation and electromagnetic waves are related via:
A) Planck's law describing spectral distribution of EM radiation ✅
B) Ohm's law
C) Newton's cooling law
D) Bernoulli's principle
27. Which part of spectrum is used for medical X-ray imaging?
A) X-rays ✅
B) Radio waves
C) Microwaves
D) Visible light
28. The group velocity can exceed phase velocity in dispersive media. True or false?
A) True (group velocity can be greater than phase velocity in anomalous dispersion) ✅
B) False
C) Only in vacuum
D) Never
29. When polarized light passes through an analyzer oriented perpendicular to the polarizer, transmitted intensity is:
A) Zero ✅ (ideal polarizers)
B) Maximum
C) Half
D) Depends on wavelength
30. Antennas transmit EM waves by converting _____ into _____.
A) AC currents into EM radiation ✅
B) DC into heat
C) Sound into light
D) Static charge into fields only
31. Faraday rotation is associated with:
A) Rotation of polarization plane in a magnetized medium ✅
B) Circular polarization creation only
C) No effect on polarization
D) Reflection
32. Which of the following waves penetrates deepest into atmosphere: radio, infrared, visible, or UV?
A) Radio waves ✅
B) UV
C) Visible
D) Infrared
33. Electromagnetic radiation pressure arises due to:
A) Momentum carried by EM waves ✅
B) Thermal expansion
C) Gravitational effects
D) Magnetic monopoles
34. In radio communication, wavelength is typically _____ compared to optical wavelengths.
A) Much larger ✅
B) Much smaller
C) Same
D) Negligible
35. Polarizers transmit components of E-field _____ to their transmission axis.
A) Parallel ✅
B) Perpendicular
C) Random
D) None
36. The photoelectric effect demonstrates particle nature of light for which part of spectrum?
A) Visible light and UV (especially UV) ✅
B) Radio waves
C) Microwaves
D) Infrared only
37. The relation between energy of a photon and its frequency is:
A) E = hf (Planck relation) ✅
B) E = hc
C) E = λ/h
D) E = h/f
38. The refractive index n of a medium is defined as:
A) n = c/v (ratio of speed in vacuum to speed in medium) ✅
B) n = v/c
C) n = λ/ f
D) n = ε0/μ0
39. Which phenomenon is responsible for the blue color of the sky?
A) Rayleigh scattering of shorter wavelengths (blue) ✅
B) Reflection from clouds
C) Polarization only
D) Absorption of red light
40. When two EM waves superpose coherently, resulting pattern can show:
A) Interference fringes ✅
B) No change
C) Only absorption
D) Only polarization
41. Which device separates light into its spectrum using diffraction?
A) Diffraction grating ✅
B) Polarizer
C) Lens
D) Prism only
42. Electromagnetic waves with wavelengths around 10^-10 m belong to:
A) X-rays ✅
B) Radio
C) Infrared
D) Visible
43. Which law describes reflection and refraction at boundaries (angle incidence equals angle reflection)?
A) Snell's law and law of reflection ✅
B) Faraday's law
C) Ampère's law
D) Gauss's law
44. Coherent light source required for clear interference patterns is typically provided by:
A) Laser ✅
B) Incandescent bulb
C) LED only
D) Sunlight only
45. In optical fibers, light is guided mainly by:
A) Total internal reflection due to core-cladding refractive index difference ✅
B) Diffraction
C) Scattering
D) Reflection from metal
46. The skin effect causes AC currents to flow near the surface of conductors at high frequency, reducing effective cross-section. True or false?
A) True ✅
B) False
C) Only for DC
D) Only in superconductors
47. Electromagnetic waves carry momentum. Radiation pressure on a perfectly absorbing surface equals:
A) I/c (intensity divided by c) ✅
B) I·c
C) I·c^2
D) Zero
48. In vacuum, phase velocity of EM waves is equal to:
A) c (speed of light) ✅
B) v_g (group velocity)
C) Infinity
D) Zero
49. The term 'polarization' cannot be applied to which type of wave?
A) Longitudinal waves (e.g., sound) ✅
B) Transverse waves
C) EM waves
D) Shear waves
50. Which of the following is a practical application of EM waves?
A) Communication, medical imaging, heating, remote sensing ✅
B) Only heat
C) Only sound propagation
D) None