The output (Y) of the circuit shown in the figure is

For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 m V/m. Given that intrinsic impedance of the free space is 120$$\pi \Omega $$, the magnitude of average power density due to this antenna at a ditance of 2 km from the antenna (in n W/$${m^2}$$) is

Match column A with column B.

Column
1. Point electromagnetic source
2. Dish antenna
3. Yagi-Uda antenna

Column
P. Highly directional
Q. End fire
R. Isotropic

If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\mathrm y}+\left(6\mathrm{xyz}\right)\widehat{\mathrm z}$$

is the electric field in a source free region, a valid expression for the electrostatic potential is