There exists a uniform electric field $E = 4 \times 10^5 \, Vm^{-1}$ directed along the negative $x$-axis such that the electric potential at the origin is zero. $A$ charge of $-200 \, \mu C$ is placed at the origin,and a charge of $+200 \, \mu C$ is placed at $(3 \, m, 0)$. The electrostatic potential energy of the system is ........... $J$.

Two capacitors of capacities $1 \mu F$ and $C \mu F$ are connected in series and the combination is charged to a potential difference of $120 \ V$. If the charge on the combination is $80 \mu C$,the energy stored in the capacitor of capacity $C$ in $\mu J$ is

In the circuit shown in the following figure,the potential difference across the $3 \mu F$ capacitor is: (in $V$)

$A$ capacitor $A$ has a capacitance of $15\ \mu F$ when filled with a dielectric of constant $K = 15$. Another capacitor $B$ is air-filled and has a capacitance of $1\ \mu F$. Both are charged to $100\ V$. After charging, the dielectric is removed from capacitor $A$, and the two capacitors are connected in parallel. The common potential difference across them will be ... $V$.

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 $\varepsilon_{r}$ is:

While working on a physics project at a school physics lab,you require a $4 \,\mu F$ capacitor in a circuit across a potential difference of $1 \,kV$. Unfortunately,$4 \,\mu F$ capacitors are out of stock in your lab,but $2 \,\mu F$ capacitors which can withstand a potential difference of $400 \,V$ are available in plenty. If you decide to use the $2 \,\mu F$ capacitors in place of the $4 \,\mu F$ capacitor,what is the minimum number of capacitors required?