An insulated conductor, initially free from charge, is charged by repeated contacts with a plate which after each contact is replenished to a charge $Q$ . If $q$is the charge on the conductor after first operation, then the maximum charge which can be given to the conductor is

Four capacitors with capacitances $C_1=1 \mathrm{\mu F},C_2=1.5 \mathrm{\mu F}$, $C_3=2.5 \mathrm{\mu F}$ and $C_4=0.5 \mathrm{\mu F}$ are connected as shown and are connected to a $30$ volt source. The potential difference between points $a$ and $b$ is:

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

A total charge $Q$ is uniformly distributed over a long rod $\mathrm{AB}$ of length $L$ as shown in the figure below. The electric potential at the point $\mathrm{O}$ lying at a distance $\frac{L}{2}$ from the end $\mathrm{A}$ is