Consider a half circular disc of radius $R$ having uniform surface charge density $\sigma .$ A disc of radius $\frac{R}{2}$ is removed from the half disc as shown in figure. Find potential at $O$ (in $V$)(centre of complete disc) $\left(\frac{\sigma R}{2{\epsilon }_0}=\frac{54\pi }{\pi -2} \mathrm{V}\right)$

Six capacitors each of capacitance $C$ is connected as shown in the figure and initially all the capacitors are uncharged. Now a battery of $\mathrm{emf} =\mathrm{\epsilon }$ is connected. How much charge will flow through the battery if the switch is on?

There are two conducting spheres of radius $a$ and $b$ $(b>a)$ carrying equal and opposite charges. They are placed at a separation $d(>>>a\mathit{ }\mathit{\&} b).$ The capacitance of the system is

Find the equivalent capacitance of the infinite ladder shown in the figure, between the points $A$ and $B$.

The figure given below shows a system of three concentric metal shells $A$, $B$ and $C$ with radii $a$, $2a$ and $3a$ respectively. Shell $B$ is earthed and the shell $C$ is given a charge $Q$. Now, if shell $C$ is connected to the shell $A$ then the final charge on the shell $B$ is equal to