$A$ charge $Q$ is uniformly distributed over the volume of an insulating sphere of radius $R$. $A$ thin metal shell of radius $b$ $(b > R)$ with a charge $-Q$ is placed around the sphere. The space between the sphere and the shell is filled with air. Which of the following graphs correctly represents the electric field $E$ as a function of distance $r$ from the center?

Two metal plates $(A, B)$ are kept horizontally with a separation of $(\frac{12}{\pi}) \text{ cm}$, with plate $A$ on the top. An atomizer jet sprays oil (density $1.5 \text{ g/cm}^3$) droplets of radius $1 \text{ mm}$ horizontally. All oil droplets carry a charge of $5 \text{ nC}$. The potentials $V_A$ and $V_B$ are required on plates $A$ and $B$ respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are . . . . . . . (Neglect the air resistance to the droplets and take $g = 10 \text{ m/s}^2$)

Two identical point charges are placed at a separation of $l$. $P$ is a point on the line joining the charges,at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $l$. Which of the following best represents the resulting curve?

The energy density $u$ is plotted against the distance $r$ from the centre of a spherical charge distribution on a $log$-$log$ scale. The slope of the obtained straight line is:

$A$ charge $Q$ of mass $m$ revolves around a charge $q$ due to the electrostatic attraction between them. The time period of its motion can be given by the formula:

Two identical balls having like charges $Q_1$ and $Q_2$ are placed at a certain distance $r$ apart and repel each other with a force $F_1$. They are brought into contact and then moved apart to a distance equal to half their initial separation $(r/2)$. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is