EM Waves — Set 3

Correct Answer: B. Tesla

• **Tesla (T)** = Magnetic flux density is measured in teslas; 1 T = 1 kg/(A·s²) = 1 V·s/m², representing a field strong enough to deflect charged particles noticeably. • **Earth's surface field ≈ 25–65 μT** — Earth's field is tens of microteslas, while medical MRI scanners use 1.5–3 T, illustrating the wide range the tesla unit covers. • 💡 Wrong-option analysis: Volt: the SI unit of electric potential difference (V = J/C), not magnetic field strength; Watt: the SI unit of power (J/s), related to energy per time — unrelated to magnetic flux density; Coulomb: the SI unit of electric charge, the source of electric fields, not magnetic flux density.

Correct Answer: C. Halved

• **Halved** = Since c = fλ and c in vacuum is constant, doubling λ requires f to halve so the product fλ remains equal to c. • **c = 3 × 10^8 m/s = constant** — This inverse relationship f ∝ 1/λ applies to all EM waves in vacuum; radio waves have large λ and low f, while gamma rays have tiny λ and very high f. • 💡 Wrong-option analysis: Four times: this would apply if λ were halved — doubling λ halves f, not quadruples it; Doubled: doubling both f and λ gives a product of 4c, violating the constancy of c; Unchanged: at constant speed, f = c/λ, so any change in λ must produce a proportional change in f.

Correct Answer: C. Transverse

• **Transverse** = Polarisation restricts oscillations to a specific direction perpendicular to propagation; this is only possible for transverse waves where the displacement is at right angles to the direction of travel. • **EM waves are transverse** — Because E and B oscillate perpendicular to the propagation direction, EM waves can be polarised; this is exploited in Polaroid sunglasses and LCD screens. • 💡 Wrong-option analysis: Stationary: the key distinction for polarisation is transverse vs. longitudinal, not stationary vs. travelling; Longitudinal: in a longitudinal wave (e.g. sound) displacement is along the propagation direction, leaving no perpendicular plane in which to restrict oscillation; Mechanical: mechanical waves can be transverse (strings) or longitudinal (sound), so 'mechanical' alone does not determine whether polarisation is possible.

Correct Answer: B. Frequency

• **Frequency** = When light crosses a boundary, frequency stays constant because it is set by the source and each photon's energy E = hf does not change at the interface. • **n = c/v** — In glass with n ≈ 1.5, speed drops to c/1.5 ≈ 2 × 10^8 m/s; since f is constant, wavelength inside glass also decreases by the same factor (λ_glass = λ_air/n). • 💡 Wrong-option analysis: Speed: light slows down in a denser medium (v = c/n) — this change in speed is precisely what causes refraction; Refractive index of air: air's n (~1.0003) is a property of air itself and is unaffected by light entering a different medium; Wavelength: wavelength decreases in proportion to the speed reduction while frequency stays constant.

Correct Answer: C. Microwaves

• **Microwaves** = Microwaves (frequencies ~300 MHz–300 GHz) are used extensively in radar and satellite communication because they penetrate clouds and rain with manageable attenuation. • **radar band ~1–10 GHz** — Radar systems and many satellite uplinks operate in this range; the short wavelengths allow compact, directional dish antennas. • 💡 Wrong-option analysis: Gamma rays: require nuclear sources, are hazardous, and cannot be practically directed for communications; Ultraviolet: strongly scattered and absorbed by the atmosphere, making it unsuitable for long-range radar or satellite links; Visible light: blocked by clouds, rain, and atmospheric scattering — unsuitable for all-weather radar and satellite communication.

Correct Answer: C. B = E/c

• **B = E/c** = Since E/B = c for a plane EM wave in vacuum, rearranging gives B = E/c. • **c = 3 × 10^8 m/s** — Because c is very large, B is numerically much smaller than E; for example, a 300 V/m electric field corresponds to B = 10^-6 T (1 μT). • 💡 Wrong-option analysis: B = E/c^2: dimensionally gives T = (V/m)/(m/s)^2 = V·s²/m³, which is not the unit of B; B = E: ignores the factor c and equates fields with different SI units; B = cE: would make B much larger than E, contradicting the relation E/B = c.

Correct Answer: D. 3.3 × 10^-19 J

• **3.3 × 10^-19 J** = Using E = hf with h = 6.63 × 10^-34 J·s and f = 5.0 × 10^14 Hz gives E = 6.63 × 10^-34 × 5.0 × 10^14 ≈ 3.3 × 10^-19 J. • **h = 6.63 × 10^-34 J·s** — This frequency (~5 × 10^14 Hz) falls in the visible green-light range; ~2 eV per photon, consistent with molecular excitation energies. • 💡 Wrong-option analysis: 3.3 × 10^-14 J: this would correspond to f ~ 5 × 10^19 Hz (hard gamma rays), not visible light; 3.3 × 10^-34 J: this is roughly equal to h itself — the result of forgetting to multiply by f; 3.3 × 10^-24 J: off by 5 orders of magnitude, corresponding to a microwave photon frequency, not visible light.

Correct Answer: A. The square of its field amplitude

• **The square of its field amplitude** = Intensity (power per unit area) of an EM wave is proportional to E₀² (or equivalently B₀²), where E₀ is the peak electric field amplitude. • **I = ½cε₀E₀²** — Doubling the field amplitude quadruples the intensity; this is analogous to power being proportional to amplitude squared in all wave types. • 💡 Wrong-option analysis: Its wavelength: wavelength determines colour/type but intensity can be the same for any wavelength — it is the amplitude, not wavelength, that sets intensity; Its speed in vacuum: c is constant for all EM waves in vacuum and does not vary with intensity; Its frequency only: frequency determines photon energy (E = hf) but not the macroscopic intensity, which depends on the number of photons (amplitude).

Correct Answer: A. Independent of frequency

• **Independent of frequency** = All EM waves travel at exactly c = 3 × 10^8 m/s in vacuum regardless of frequency — radio waves, visible light, and gamma rays all travel at the same speed. • **c = 3 × 10^8 m/s** — This is a fundamental consequence of Maxwell's equations; frequency only determines wavelength (λ = c/f), not the wave speed. • 💡 Wrong-option analysis: Zero for radio waves: all EM waves including radio travel at c in vacuum — zero speed would mean no propagation at all; Greater for lower frequency: speed is constant, independent of frequency — lower frequency only means longer wavelength; Greater for higher frequency: speed is constant, independent of frequency — higher frequency only means shorter wavelength.

Correct Answer: B. Radio < Microwave < Infrared < Visible < Ultraviolet < X-ray < Gamma

• **Radio < Microwave < Infrared < Visible < Ultraviolet < X-ray < Gamma** = Frequency increases progressively from radio (lowest, ~kHz–GHz) through microwave, IR, visible, UV, X-ray, to gamma (highest, >10^19 Hz). • **c = fλ** — Since wavelength decreases as frequency increases at fixed c, this order is also the order of decreasing wavelength from radio to gamma. • 💡 Wrong-option analysis: Gamma < X-ray < UV < Visible < IR < Microwave < Radio: this is the correct order reversed — it lists decreasing frequency, not increasing; Visible < IR < UV < Microwave < X-ray < Radio < Gamma: IR has lower frequency than visible, and radio has lower frequency than X-ray, so this order is internally inconsistent; Infrared < Radio < Microwave < Visible < X-ray < UV < Gamma: radio has lower frequency than IR, not higher, making this sequence wrong.