A rectangular waveguide having $$T{E_{10}}$$ mode as dominant mode is having a cutoff frequency of 18 GHz for the $$T{E_{30}}$$ mode. The inner broad-wall dimension of the rectangular waveguide is

When a plane wave traveling in free-space is incident normally on a medium having $${\varepsilon _r} = 4.0,$$ the fraction of power transmitted into the medium is given by

A medium is divided into regions $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ about $$x = 0$$ plane, as shown in the Fig. below. An electromagnetic wave with electric field $${\overrightarrow E _1} = 4{\widehat a_x} + 3{\widehat a_y} + 5{\widehat a_z}$$ is incident normally on the interface form region-$${\rm I}$$ . The electric field $${E_2}$$ in region-$${\rm I}$$$${\rm I}$$ at the interface is

$$\nabla \times \nabla \times P$$, where P is a vector, is equal to