Uniform Plane Waves Questions and Answers

Answer: C

Correct answer: the electric and magnetic fields within it are in phase

That is the false one. Because the intrinsic impedance of a good conductor carries a 45 degree phase angle, the magnetic field lags the electric field by 45 degrees inside the metal. The other three are all correct: the 45 degree angle itself, the decay to \( 1/e \) - about a third - in one skin depth, and the equality \( \alpha = \beta = 1/\delta \).

Answer: D

Polarisation mismatch cannot be overcome by power, since the field has no component along the antenna, so the antenna must be turned or a circularly polarised one used. Circular polarisation costs three decibels against a matched linear pair but is immune to orientation.

Answer: A

Metal reflects almost perfectly, but the reflection is specular, so a surface angled away sends the energy elsewhere and little returns to the receiver. Shaping to achieve exactly that is the principle of a low-observable aircraft.

Answer: B

Sea water is a good conductor at a megahertz and the skin depth is of the order of a quarter of a metre, so the field falls by a factor of e in that distance. Communication with a submerged submarine therefore uses very low frequencies, where the skin depth is tens of metres.

Answer: C

The convention takes the electric field as defining the polarisation, so the plane of polarisation holds that field and the propagation direction. The magnetic field is perpendicular to that plane, and an antenna must be aligned with the electric field to receive.

Answer: D

Nothing along the path can change how often the field reverses, so the frequency is carried unchanged from medium to medium. The wavelength and the velocity both adjust to the medium, which is the whole content of refraction.

Answer: A

The three vectors form a right-handed set in the order electric field, magnetic field, direction of propagation, so the magnetic field must lie along the remaining axis. Reversing the direction of travel would reverse the magnetic field while leaving the electric field alone.

Answer: B

Free electrons make its effective relative permittivity less than one and frequency dependent, so the phase velocity exceeds c and the wave bends away from the vertical. That bending is what returns short waves to earth and makes long-distance broadcasting possible.

Answer: C

The effective permittivity falls to zero at that frequency, the wave can go no further and it returns. Above it the wave passes through, which is why satellite links use frequencies well above the critical value and broadcast services below it.

Answer: D

A few micrometres of aluminium is many skin depths at a gigahertz, so a metallised plastic film screens as well as a sheet of metal. At mains frequency, by contrast, several millimetres of copper are needed and high permeability material is preferred.