A region shown below contains a perfect conducting half-space and air. The surface current $${\overrightarrow K _{_s}}$$ on the surface of the perfect conductor is $${\overrightarrow K _{_s}} = \widehat x\,2$$ amperes per meter. The tangential $$\overrightarrow H $$ field in the air just above the perfect conductor is

Assume that a plane wave in air with an electric field
$$\overrightarrow E = 10\cos \left( {\omega t - 3x - \sqrt {3z} } \right){\widehat a_{_y}}\,\,\,V/m$$ is incident
on a non-magnetic dielectric slab of relative permittivity $$3$$ which covers the region $$z > 0$$ . The angle of transmission in the dielectric slab is _______ degrees.

Consider an air filled rectangular waveguide with a cross-section of $$5\,\,cm\,\, \times \,\,3\,cm$$. For this waveguide, the cut-off frequency (in MHz) of $$T{E_{21}}\,$$ mode is __________________

A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to