Miscellaneous · Electromagnetics · GATE ECE

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link

Light from free space is incident at an angle $${\theta _1}$$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are $${n_1}\,\, = \,\,1.5$$ and $${n_2}\,\, = \,\,1.4$$ respectively.

The maximum value of $${\theta _1}$$ (in degrees) for which the incident light will be guided in the core of the fibre is ________ .

A square metal sheet of $4 \mathrm{~m} \times 4 \mathrm{~m}$ is placed on the $x-y$ plane as shown in the figure below. If the surface charge density (in $\mu \mathrm{C} / \mathrm{m}^2$ ) on the sheet is $\rho_s(x, y)=4|y|$, then the total charge (in $\mu \mathrm{C}$, rounded off to the nearest integer) on the sheet is___________ .

The permittivity of water at optical frequencies is $$1.75{\varepsilon _0}$$. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius $$5m$$, as shown in the figure. The critical angle is $${\theta _c}$$

The value of $$d$$ (in meter) is ______ .

An optical fiber is kept along the$$\widehat Z$$ direction. The refractive indices for the electric fields along $$\widehat X$$ and $$\widehat Y$$ directions in the fiber are $${n_x} = 1.5000$$ and $${n_y} = 1.5001$$, respectively ($${n_x} \ne {n_y}$$ due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is $$1.5\,\,\,\mu m$$. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters, is _______ .

A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is aligned for maximum directional radiation and reception to a target 1 km away having radar cross-section of 3m². If it transmits 100 kW, then the received power (in $$\mu W$$) is ______ .