The four identical capacitors in the circuit shown below are initially uncharged. The switch is then thrown first to position $A$, and then to position $B$. After this is done:
Note: $V_{1,2,3,4}$ are the potential differences across $C_{1,2,3,4}$ and $Q_{1,2,3,4}$ are the final charges stored in $C_{1,2,3,4}$ respectively.

$A$ combination of capacitors is set up as shown in the figure. The magnitude of the electric field,due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4 \mu F$ and $9 \mu F$ capacitors),at a point distance $30 \ m$ from it,would equal ....... $N/C$.

Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. $A$ number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius $r \ll h$. Now a high voltage source $(HV)$ is connected across the conducting plates such that the bottom plate is at $+V_0$ and the top plate at $-V_0$. Due to their conducting surface,the balls will get charged,will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate,where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)
$(1)$ Which one of the following statements is correct?
$(A)$ The balls will stick to the top plate and remain there
$(B)$ The balls will bounce back to the bottom plate carrying the same charge they went up with
$(C)$ The balls will bounce back to the bottom plate carrying the opposite charge they went up with
$(D)$ The balls will execute simple harmonic motion between the two plates
$(2)$ The average current in the steady state registered by the ammeter in the circuit will be
$(A)$ zero
$(B)$ proportional to the potential $V_0$
$(C)$ proportional to $V_0^{1/2}$
$(D)$ proportional to $V_0^2$

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$. $(i)$ The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is $E_1$. (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$. Then,the value of $E_1 / E_2$ is:

$n$ small drops of the same size are charged to $V$ volts each. If they coalesce to form a single large drop,then its potential will be:

The potential differences that must be applied across the parallel and series combination of $3$ identical capacitors are such that the energy stored in them becomes the same. The ratio of the potential difference in the parallel combination to the series combination is: