Some unknown material has a conductivity of $${10^{ 6}}$$ $$mho/m$$ and a permeability of $$4\pi \times {10^{ - 7}}\,\,\,\,\,H/m.$$ The skin depth for the material at $$1GHz$$ is

A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m² is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of the cube is

A uniform plane wave having parallel polarization is obliquely incident on an air - dielectric interface as shown in Fig. If the wave has an electric field $$E = 10\,\,V/m$$, find
(i) The angle of incidence $${\theta _i}$$ for which there is no reflection of the wave.
(ii) The surface charge density at the interface.

A transverse electromagnetic wave with circular polarization is received by a dipole antenna. Due to polarization mismatch, the power transfer efficiency from the wave to the antenna is reduced to about