Two metal spheres of radii $0.01 \ m$ and $0.02 \ m$ are given a charge of $15 \ mC$ and $45 \ mC$ respectively. They are then connected by a wire. The final charge on the first sphere is $\ldots \ldots \ldots \times 10^{-3} \ C$.

$A$ conducting body $1$ has some initial charge $Q$,and its capacitance is $C$. There are two other conducting bodies,$2$ and $3$,having capacitances $C_2 = 2C$ and $C_3 \rightarrow \infty$. Bodies $2$ and $3$ are initially uncharged. Body $2$ is touched with body $1$. Then,body $2$ is removed from body $1$ and touched with body $3$,and then removed. This process is repeated $N$ times. The charge on body $1$ at the end must be:

In the circuit shown,$C_1 = 6\,\mu F, C_2 = 3 \,\mu F$ and battery $B = 20\,V$. The switch $S_1$ is first closed. It is then opened and afterwards $S_2$ is closed. What is the charge (in $\mu C$) finally on $C_2$?

$A$ $4 \mu F$ capacitor is charged by a $200 \ V$ battery. It is then disconnected from the supply and connected to another uncharged $2 \mu F$ capacitor. During the process,the loss of energy (in $J$) is:

$A$ capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system:

$A$ $600\; pF$ capacitor is charged by a $200\; V$ supply. It is then disconnected from the supply and is connected to another uncharged $600\; pF$ capacitor. How much electrostatic energy is lost in the process?