A long cylinder of radius R carries a magnetization M⃗ = kρ2φ̂, where k is a constant, ρ is the radial distance from the axis, and φ̂ is the azimuthal unit vector. The magnetic field inside and outside the cylinder would be:

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: