Consider an infinite matrix of capacitors as shown in the figure. The effective capacitance between point $A$ and $B$ will be

For the circuit shown in the figure,the charge on the $4 \mu F$ capacitor is $....... \mu C$.

$A$ capacitor,$C_1 = 6 \ \mu F$ is charged to a potential difference of $V_0 = 5 \ V$ using a $5 \ V$ battery. The battery is removed and another capacitor,$C_2 = 12 \ \mu F$ is inserted in place of the battery. When the switch $S$ is closed,the charge flows between the capacitors for some time until an equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when the equilibrium condition is reached?

$A$ capacitor $C_1 = 1\,\mu F$ can withstand a maximum voltage of $V_1 = 6\,kV$,and a capacitor $C_2 = 3\,\mu F$ can withstand a maximum voltage of $V_2 = 4\,kV$. If these two capacitors are connected in series,what is the maximum voltage (in $kV$) that can be applied to the combination?

$(a)$ Determine the electrostatic potential energy of a system consisting of two charges $7 \; \mu C$ and $-2 \; \mu C$ (with no external field) placed at $(-9 \; cm, 0, 0)$ and $(9 \; cm, 0, 0)$ respectively.
$(b)$ How much work is required to separate the two charges infinitely away from each other?
$(c)$ Suppose that the same system of charges is now placed in an external electric field $E = A(1/r^2)$; $A = 9 \times 10^5 \; C \cdot m^{-2}$. What would the electrostatic energy of the configuration be?

$A$ parallel-plate capacitor is connected to a cell. Its positive plate $A$ and its negative plate $B$ have charges $+Q$ and $-Q$ respectively. $A$ third plate $C$, identical to $A$ and $B$, with charge $+Q$, is now introduced midway between $A$ and $B$, parallel to them. Which of the following are correct?