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 ........... $J$.

Four capacitors,each of capacity $3\,\mu F$,are connected as shown in the adjoining figure. The ratio of the equivalent capacitance between $A$ and $B$ to that between $A$ and $C$ will be:

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?

Two capacitors of capacitances $1\ \mu F$ and $3\ \mu F$ are charged to the same voltages $5\ V$. They are connected in parallel with oppositely charged plates connected together. Then:

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

In the circuit shown in the figure,four capacitors are connected to a battery. $A$ parallel plate capacitor has an electric field of $10^5 \ V/m$ between its plates. If the charge on the capacitor plate is $1 \ \mu C$,then the force on each capacitor plate is.....$N$.