An antenna with a directive gain of 6 dB is radiating a total power of 16 kw . The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of 6 dB gain(rounded off to three decimal places is$\_\_\_\_$ $\mathrm{V} / \mathrm{m}$.

A standard air-filled rectangular waveguide with dimensions $a=8 \mathrm{~cm}, b=4 \mathrm{~cm}$, operates at 3.4 GHz . For the dominant mode of wave propagation, the phase velocity of the signal is $v_p$. The value (rounded off to two decimal places) of $v_p / c$, where $c$ denotes the velocity of light, is $\_\_\_\_$ .

The vector function $F(r) = -x \hat{i} + y \hat{j}$ is defined over a circular arc C shown in the figure,

The line integral of $\int\limits_{C} \mathbf{F(r)} \cdot d\mathbf{r}$ is