For a $GPS$ navigation to track a mobile device,we use :-

The electric field of a plane electromagnetic wave is given by $\overrightarrow{E} = E_{0} \frac{\hat{i}+\hat{j}}{\sqrt{2}} \cos (kz+\omega t)$. At $t=0$,a positively charged particle is at the point $(x, y, z) = (0, 0, \frac{\pi}{k})$. If its instantaneous velocity at $t=0$ is $v_{0} \hat{k}$,the force acting on it due to the wave is

$A$ physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$,where $\vec{E}$ is the electric field,$\vec{B}$ is the magnetic field,and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity(ies)?
$(A)$ $\frac{\text{Energy}}{\text{charge} \times \text{current}}$
$(B)$ $\frac{\text{Force}}{\text{Length} \times \text{Time}}$
$(C)$ $\frac{\text{Energy}}{\text{Volume}}$
$(D)$ $\frac{\text{Power}}{\text{Area}}$

The dimensional formula for the physical quantity $\frac{E^2 \mu_0 \varepsilon_0}{B^2}$ is ($E =$ electric field and $B =$ magnetic field).

Generation,propagation,and detection of electromagnetic waves is the basis of:

If two linear antennas having lengths in the ratio $2: 3$ are emitting radiation of wavelengths in the ratio $8: 9$, then the ratio of effective powers radiated by them are in the ratio