Can the following scalar and vector potentials describe an electromagnetic field? φ(x, t) = 3xyz - 4t and A(x, t) = (2x - ωt)î + (y - 2z)ĵ + (z - 2eiωt)k̂, where ω is a non-zero constant.

A long rectangular metallic loop of width W and length L (L ≫ W) starts entering a region where there is a uniform magnetic field B perpendicular to the plane of the loop. The resistance of the loop is R and its mass is M. If v0 is the velocity of the loop just before entering the region, then neglecting self-inductance effects, the velocity at a later time t is:

Electromagnetic waves of frequency ω are incident on an electron gas whose relaxation time is τ. Let σlow and σhigh represent the respective electrical conductivities of the gas in low frequency (ωτ ≪ 1) and high frequency (ωτ ≫ 1) limits. The ratio (σlow / σhigh) is: