An infinitely long thin wire carrying a uniform linear static charge density λ is placed along the z-axis (Fig. 8.1). The wire is set into motion along its length with a uniform velocity . Calculate the poynting vector .

What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant.

What geometrical characteristic of LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

Even though an electric field E exerts a force qE on a charged particle yet the electric field of an EM wave does not contribute to the radiation pressure (but transfers energy). Explain.

Sea water at frequency v = 4 × 108 Hz has permittivity ε ≈ 80 ε_o, permeability μ ≈ μo and resistivity ρ = 0.25 Ω–m. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source. What fraction of the conduction current density is the displacement current density?

A long straight cable of length l is placed symmetrically along z-axis and has radius a(<<l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is

(i) Calculate the displacement current density inside the cable.

(ii) Integrate the displacement current density across the cross section of the cable to find the total displacement current Id.

(iii) Compare the conduction current I₀ with the displacement current .