EM Waves — Set 1

Correct Answer: A. c = fλ

• **c = fλ** = The fundamental wave equation states speed equals frequency multiplied by wavelength, giving c = fλ for EM waves in vacuum. • **c = 3 × 10^8 m/s** — This universal constant links any EM wave's frequency and wavelength; at fixed c, higher frequency means shorter wavelength. • 💡 Wrong-option analysis: c = λ/f: inverts the roles of f and λ, giving units of m²/s not m/s; c = f + λ: adds incompatible units (Hz + m), which is physically meaningless; c = f/λ: gives units of Hz/m, not m/s.

Correct Answer: A. Mutually perpendicular, with E and B both perpendicular to propagation

• **Mutually perpendicular** = In a plane EM wave, E and B are perpendicular to each other and both are also perpendicular to the direction of propagation, making EM waves transverse. • **S = E × B/μ₀** — The Poynting vector, given by the cross product E × B, points along the propagation direction, confirming the three-way perpendicularity. • 💡 Wrong-option analysis: E perpendicular to B but both parallel to propagation: EM waves are transverse not longitudinal — fields cannot be parallel to propagation; E parallel to propagation and B perpendicular: the electric field is always transverse, never along the propagation axis; All parallel to each other: this would require a scalar wave with no oscillation direction, which EM waves are not.

Correct Answer: C. Radio waves

• **Radio waves** = Radio waves occupy the lowest-frequency, longest-wavelength end of the EM spectrum, with wavelengths ranging from millimetres to kilometres. • **wavelengths up to ~10^3 m** — Radio waves can have wavelengths of hundreds of metres; since c = fλ and c is fixed, their frequencies are the lowest (~kHz to GHz range). • 💡 Wrong-option analysis: Ultraviolet: UV wavelengths are ~10–400 nm, far shorter than radio waves; Gamma rays: gamma rays have the shortest wavelengths (~10^-12 m), the opposite extreme of the spectrum; X-rays: X-rays range ~0.01–10 nm, vastly shorter than radio waves.

Correct Answer: A. Infrared

• **Infrared** = TV remote controls transmit signals using near-infrared radiation (around 940 nm wavelength), which is invisible to the human eye but easily detected by the receiver sensor. • **~940 nm wavelength** — This near-IR wavelength is safe, inexpensive to produce with LEDs, and does not interfere with visible broadcasts or radio signals. • 💡 Wrong-option analysis: Gamma rays: highly penetrating ionising radiation used in nuclear/medical contexts — far too energetic and hazardous for a household remote; X-rays: ionising radiation used for medical imaging, not suitable for domestic consumer electronics; Ultraviolet: UV photons carry more energy than IR and can cause tissue damage; UV LEDs for this purpose are also costlier and less efficient.

Correct Answer: D. Gamma rays

• **Gamma rays** = Gamma rays sit at the extreme high-frequency end of the EM spectrum, with frequencies typically above 10^19 Hz and photon energies in the MeV range. • **f > 10^19 Hz** — Because E = hf, gamma photons carry the greatest energy per photon of any EM radiation, making them the most penetrating and ionising. • 💡 Wrong-option analysis: Microwaves: frequencies ~300 MHz–300 GHz, many orders of magnitude lower than gamma rays; Radio waves: the lowest-frequency EM radiation (~kHz to GHz), at the opposite end of the spectrum; Infrared: frequencies ~300 GHz–400 THz, well below visible light and far below gamma rays.

Correct Answer: C. c

• **c** = For any plane EM wave in vacuum, the ratio of electric field amplitude to magnetic field amplitude equals the speed of light: E/B = c. • **c = 3 × 10^8 m/s** — Since c is very large, E (in V/m) is numerically much larger than B (in T) for the same wave; this ratio follows directly from Maxwell's equations. • 💡 Wrong-option analysis: c^2: dimensionally incorrect — E/B has units of m/s, not m²/s²; 1: would imply E and B have the same numerical value, but their SI units differ and c ≠ 1 in SI; 1/c: gives E = B/c, implying B > E numerically, which contradicts Maxwell's equations for a vacuum wave.

Correct Answer: A. Hertz

• **Hertz (Hz)** = The SI unit of frequency is the hertz, defined as one complete cycle of oscillation per second. • **1 Hz = 1 s⁻¹** — Named after Heinrich Hertz; EM wave frequencies range from ~10^3 Hz (radio) to ~10^25 Hz (highest gamma rays), all expressed in hertz. • 💡 Wrong-option analysis: Meter: the SI unit of wavelength (length), not frequency; Joule: the SI unit of energy — frequency and energy are related by E = hf but joule is not the unit of frequency; Tesla: the SI unit of magnetic flux density B, an entirely different physical quantity.

Correct Answer: A. Accelerate

• **Accelerate** = An accelerating electric charge radiates energy as EM waves; this is the fundamental mechanism behind all EM emission, from radio antennas to X-ray tubes. • **Larmor formula: P ∝ a²** — Radiated power is proportional to the square of the acceleration; a stationary or uniformly moving charge produces no EM radiation. • 💡 Wrong-option analysis: Remain at rest: a static charge creates only a static Coulomb field — no changing fields, no EM wave; Move with constant velocity only: uniform motion produces no radiation as confirmed by classical electrodynamics; Have zero mass: mass is irrelevant to radiation — photons are massless yet EM radiation is produced by massive charged particles.

Correct Answer: C. Ultraviolet

• **Ultraviolet** = UV radiation (200–400 nm) carries sufficient photon energy to break chemical bonds in DNA and skin-cell proteins, causing sunburn and increasing skin-cancer risk. • **UV-B (280–315 nm)** — UV-B photons are most responsible for sunburn; the ozone layer absorbs a large fraction of UV-B, making ozone depletion a serious public health concern. • 💡 Wrong-option analysis: Radio waves: photon energy ~10^-7 eV — far too low to ionise molecules or damage tissue; Infrared: IR delivers warmth but lacks the photon energy needed to break DNA bonds and cause sunburn; Microwaves: slightly more energetic than radio but still far below the threshold for photochemical skin damage.

Correct Answer: D. 2.45 GHz

• **2.45 GHz** = Household microwave ovens use 2.45 GHz radiation, a microwave-band frequency that is efficiently absorbed by water molecules in food. • **λ ≈ 12.2 cm** — At 2.45 GHz the wavelength is about 12 cm; this frequency is internationally allocated for industrial, scientific, and medical (ISM) use, avoiding interference with communications. • 💡 Wrong-option analysis: 30 MHz: this is the HF radio band — far too low a frequency to heat food efficiently via molecular rotation; 500 THz: this is the frequency of visible green light, not microwaves; 50 Hz: this is the mains electricity supply frequency, not an EM radiation frequency used for cooking.