$A$ conducting sphere of radius $a$ has charge $Q$ on it. It is enclosed by a neutral conducting concentric spherical shell having inner radius $2a$ and outer radius $3a$. Find the electrostatic energy of the system.

$A$ parallel plate capacitor of capacity $100 \mu F$ is charged by a battery of $50 \text{ V}$. The battery remains connected and if the plates of the capacitor are separated so that the distance between them becomes double the original distance,the additional energy given by the battery to the capacitor in joules is

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4 R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is: (Take $k=\frac{1}{4 \pi \epsilon_0}$ and assume $k Q^2 > G m^2$ where $G$ is the Gravitational constant)

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same total energy stored in it as the first combination has. The value of $C_2$ in terms of $C_1$ is:

Show that for a combination of capacitors in series or parallel,the total energy stored is the sum of the energies stored in individual capacitors.

In the given circuit,$C_1=2\,\mu F, C_2=0.2\,\mu F, C_3=2\,\mu F, C_4=4\,\mu F, C_5=2\,\mu F, C_6=2\,\mu F$. The charge stored on capacitor $C_4$ is $.....\mu C$.