The electric field intensity produced by the radiation coming from a $100 \, W$ bulb at a distance of $3 \, m$ is $E$. The electric field intensity produced by the radiation coming from a $60 \, W$ bulb at the same distance is $\sqrt{\frac{x}{5}} E$. The value of $x$ 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 graph between radiation power $P$ from a linear antenna and the square of the length of the antenna $l^2$ is shown in the figure for two antennas $A$ and $B$. If all other parameters are the same,find the ratio of the wavelengths of $A$ and $B$,i.e.,$\frac{\lambda_A}{\lambda_B}$.

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

$A$ parallel plate capacitor has a capacitance $C = 200 \ pF$. It is connected to a $230 \ V$ $AC$ supply with an angular frequency $\omega = 300 \ rad/s$. The $rms$ value of the conduction current in the circuit and the displacement current in the capacitor,respectively,are:

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