Electromagnetic Waves — Exam Practice

Answer Displacement current has the SI unit ampere — exactly the same as conduction current. This is intentional: Maxwell defined it so that the two could be added directly in the Ampere–Maxwell Law.

Answer Displacement current is defined as I_d = ε₀(dΦ_E/dt) — a term equivalent to a current, arising from a changing electric field, even where no actual charge is physically moving.

The modified law: ∮B·dl = μ₀I_c + μ₀ε₀(dΦ_E/dt).

It's needed because plain Ampere's Law gives inconsistent results for a charging capacitor, depending on which surface is chosen for the Gaussian loop — some surfaces (passing between the plates) enclose no conduction current at all. Adding displacement current resolves this inconsistency completely.

Answer (a) In order of increasing frequency: Radio waves (broadcasting) → Microwaves (radar, ovens) → Infrared (remote controls, thermal imaging) → Visible light (vision) → Ultraviolet (sterilization) → X-rays (medical imaging) → Gamma rays (cancer treatment).

(b) I_d = ε₀A(dE/dt) = 8.85×10⁻¹² × π×(0.01)² × 10¹³.
= 8.85×10⁻¹² × 3.1416×10⁻⁴ × 10¹³ ≈ 0.0278 A ≈ 27.8 mA.

Solution Microwaves' shorter wavelength (compared to radio) allows for more focused beams and finer resolution, making them well-suited to radar and satellite communication.

Solution Averaged over a full oscillation, energy density u_E = ½ε₀E² equals u_B = B²/2μ₀ — a clean, symmetric split.

Solution A steadily moving charge produces a static-looking field pattern that simply translates with it — genuine radiation requires acceleration, such as the oscillating current in a radio antenna.

Solution X-rays sit well beyond ultraviolet in the spectrum — much shorter wavelength and correspondingly much higher frequency and photon energy than visible light.

Solution λ = c/f = (3×10⁸) / (6×10¹⁴) = 5×10⁻⁷ m = 500 nm — squarely in the visible range (green-blue light).

Solution E₀ = cB₀ always holds for an EM wave in vacuum — the amplitude ratio is fixed by the speed of light itself, not free to vary independently.

Solution For the Ampere–Maxwell Law to give consistent results regardless of which Gaussian surface is chosen, displacement current must exactly equal conduction current: I_d = I_c = 0.5 A.