EM Waves — Set 2

Correct Answer: B. E = hf

• **E = hf** = Planck's relation states that the energy of a photon equals Planck's constant multiplied by the frequency of the radiation. • **h = 6.63 × 10^-34 J·s** — This tiny constant bridges quantum and classical physics; a gamma-ray photon (~10^20 Hz) carries roughly 10^17 times more energy than a radio photon (~10^3 Hz). • 💡 Wrong-option analysis: E = h/λ: the correct form is E = hc/λ (using c = fλ) — writing just h/λ omits the factor c and is dimensionally wrong; E = hf/c: gives units of J·s·Hz/(m/s) = J/m, not joules; E = mc: has units of kg·m/s (momentum), not energy — Einstein's correct mass-energy relation is E = mc².

Correct Answer: C. Do not require a material medium

• **Do not require a material medium** = EM waves propagate through vacuum via mutually sustaining oscillating electric and magnetic fields, requiring no matter to carry them. • **c = 3 × 10^8 m/s in vacuum** — Sunlight travels ~150 million km through the vacuum of space to reach Earth, directly demonstrating that EM waves need no medium. • 💡 Wrong-option analysis: Need solid particles to transfer energy: that describes phonons or elastic waves, not EM radiation; Need water vapor to propagate: water vapour actually absorbs certain IR and microwave frequencies, impeding rather than aiding propagation; Require air molecules to vibrate: that is the mechanism for sound (mechanical) waves, which cannot travel through vacuum.

Correct Answer: A. Energy flow in the EM wave

• **Energy flow in the EM wave** = The Poynting vector S = (1/μ₀)(E × B) points in the direction of energy transport and has magnitude equal to the wave's intensity (power per unit area). • **S = E × B/μ₀** — For a wave travelling along +z with E along x̂ and B along ŷ, S points along +ẑ, confirming it gives the propagation and energy-flow direction. • 💡 Wrong-option analysis: Wavelength increase: wavelength is a scalar property — the Poynting vector gives no information about wavelength changes; Magnetic field only: B is an input to compute S, not what S itself represents; Electric field only: E is also just an input — only the cross product E × B together gives the energy-flow direction.

Correct Answer: A. 3 m

• **3 m** = Using λ = c/f with c = 3 × 10^8 m/s and f = 10^8 Hz gives λ = 3 × 10^8 / 10^8 = 3 m. • **100 MHz = FM radio band** — Wavelengths around 3 m correspond to the FM broadcast band; a quarter-wave antenna for this frequency would be about 0.75 m long. • 💡 Wrong-option analysis: 0.03 m: this corresponds to f = 10 GHz (microwave band), ten times higher than 100 MHz; 30 m: this corresponds to f = 10 MHz (shortwave band), ten times lower than 100 MHz; 0.3 m: this corresponds to f = 1 GHz (UHF), ten times higher than 100 MHz.

Correct Answer: A. Sound waves

• **Sound waves** = Sound is a mechanical longitudinal pressure wave requiring a material medium such as air, water, or solid to propagate — it is not electromagnetic in nature. • **speed ~343 m/s in air** — Sound travels at ~343 m/s at room temperature, about one million times slower than light, and cannot travel through vacuum unlike EM waves. • 💡 Wrong-option analysis: Radio waves: genuine EM waves used for communication, travelling at c in vacuum; Visible light: EM waves with wavelength 400–700 nm, directly part of the electromagnetic spectrum; X-rays: high-energy EM waves (~0.01–10 nm) used in medical imaging, fully electromagnetic.

Correct Answer: B. 400–700 nm

• **400–700 nm** = The human eye detects EM radiation in the approximate range 400 nm (violet) to 700 nm (red), constituting visible light. • **violet ~400 nm, red ~700 nm** — This corresponds to frequencies of ~430 THz (red) to ~750 THz (violet); this narrow band sits between UV and infrared in the EM spectrum. • 💡 Wrong-option analysis: 0.1–10 nm: this is the X-ray/extreme-UV range, far too short for the eye to detect; 1–100 m: this is the radio/TV broadcast wavelength range, at the opposite long-wavelength end of the spectrum; 1–10 mm: this is the microwave/millimetre-wave range, well above visible-light wavelengths.

Correct Answer: B. X-rays

• **X-rays** = X-rays (wavelength ~0.01–10 nm) are absorbed much more strongly by dense bone than by soft tissue, creating high-contrast images on a detector placed behind the patient. • **~20–100 keV photon energy** — Diagnostic X-rays use photons in this energy range, optimised for bone-to-tissue contrast without excessive radiation dose. • 💡 Wrong-option analysis: Microwaves: too long a wavelength to resolve bone structures, and largely absorbed by water in tissue — not useful for bone imaging; Radio waves: MRI uses radio frequencies to detect hydrogen nuclei signals, not bone density — plain bone radiography specifically means X-rays; Infrared: penetrates only ~1 mm into tissue, making it useless for imaging internal structures such as bones.

Correct Answer: B. In phase with each other

• **In phase with each other** = In a plane EM wave, E and B reach their maximum, zero, and minimum values simultaneously — they oscillate in phase with zero phase difference. • **E = cB at every instant** — This instantaneous relationship holds at every point and time; both fields peak and vanish together, confirming zero phase difference. • 💡 Wrong-option analysis: Randomly changing with no relation: E and B are tightly coupled through Maxwell's equations and always maintain the ratio E/B = c; Always 90° out of phase: a 90° phase shift would cause energy to oscillate in and out of the fields rather than being transported, contradicting travelling-wave behaviour; Opposite in direction but same axis: E and B are mutually perpendicular, not anti-parallel, and both are perpendicular to the propagation direction.

Correct Answer: D. Maxwell

• **Maxwell** = James Clerk Maxwell unified electricity and magnetism in four equations (1864) and predicted that coupled oscillating E and B fields would propagate as waves at speed 1/√(μ₀ε₀). • **1/√(μ₀ε₀) ≈ 3 × 10^8 m/s** — Maxwell found this theoretical speed matched the measured speed of light, leading him to conclude that light itself is an electromagnetic wave. • 💡 Wrong-option analysis: Newton: proposed the corpuscular theory of light and predates the concept of EM field waves by two centuries; Bohr: developed atomic models and the quantum theory of hydrogen spectra, not EM wave theory; Galileo: made foundational contributions to mechanics and astronomy but lived two centuries before Maxwell.

Correct Answer: C. Hertz

• **Hertz** = Heinrich Hertz in 1887–88 produced radio waves with a spark-gap transmitter and detected them with a resonant loop receiver, directly confirming Maxwell's prediction. • **Year 1887** — Hertz also showed these waves could be reflected, refracted, and polarised like light, proving they belonged to the same class of phenomena Maxwell described. • 💡 Wrong-option analysis: Faraday: discovered electromagnetic induction and pioneered field concepts but did not experimentally produce or detect EM waves; Einstein: explained the photoelectric effect (1905) and developed relativity — Hertz's demonstrations preceded Einstein by two decades; Rutherford: famous for the nuclear model of the atom (1911), not for EM wave experiments.