Two positive charges of magnitude $q$ are placed at the ends of one side of a square of side $2a$. Two negative charges of the same magnitude are kept at the other two corners. Starting from rest,if a charge $Q$ moves from the midpoint of the side with positive charges to the centre of the square,its kinetic energy at the centre of the square is

Three identical capacitors $C_1, C_2$ and $C_3$ have a capacitance of $1.0 \mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity $\varepsilon_r$. The cell electromotive force (emf) $V_0 = 8 \ V$. First,the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged,$S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium,the charge on $C_3$ is found to be $5 \mu C$. The value of $\varepsilon_r = . . . . $

Three charged capacitors,$C_1 = 17 \ \mu F$,$C_2 = 34 \ \mu F$,$C_3 = 41 \ \mu F$ and two open switches,$S_1$ and $S_2$ are assembled into a network with initial voltages and polarities,as shown in the figure. The final status of the network is attained when the two switches,$S_1$ and $S_2$ are closed. In the figure,the final charge on capacitor $C_3$ in $mC$ is closest to:

$A$ soap bubble of radius $R$ and surface tension $T$ is formed in a vacuum. It is slowly charged so that it slowly expands. It stops charging when the radius becomes $2R$. Find the amount of charge given to the bubble.

Four capacitors of capacitance $10\,\mu F$ and a battery of $200\, V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed? (in $\mu C$)

In the given capacitive network,the resultant capacitance between points $A$ and $B$ is: (in $\mu F$)