A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \right){\mkern 1mu} {\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$ is incident on a perfectly conducting slab positioned at $$x \le 0$$. The $$\overrightarrow E $$ field of the reflected wave is

A transmission line with a characteristic impedance of 100 $$\Omega $$ is used to match a 50 $$\Omega $$ section to a 200 $$\Omega $$ section. If the matching is to be done both at 429 MHz and 1 GHz, the tength of the transmission line can be approximately

The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the figure is $${H_Z} = 3\,\,\cos \,\,(2.094\,\, \times \,\,{10^2}x)\,\,\,\cos \,(2.618\,\, \times \,\,{10^2}y)$$
$$\cos \,\,(6.283\,\, \times \,\,{10^{10}}t\, - \beta \,z)$$
The phase velocity $${V_p}$$ of the wave inside the waveguide satisfies

The radiation pattern of an antenna in spherical co-ordinates is given by $$$F\,(\theta )\, = {\cos ^4}\,\theta \,\,\,;\,\,0\,\, \le \,\,\theta \,\, \le \,\,\pi /2$$$ The directivity of the antenna is