$A$ metal sphere of radius $1 \ m$ is charged with $10^{-2} \ C$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \ N/m^2$. The volume strain in the sphere is $(\epsilon_{0} = \text{permittivity of free space})$

For the circuit shown in the figure,the charge on the $4 \mu F$ capacitor is $....... \mu C$.

$A$ soap bubble of radius $R$ and surface tension $T$ is formed in a vacuum. It is slowly charged so that it slowly expands. It stops charging when the radius becomes $2R$. Find the amount of charge given to the bubble.

Two capacitors of $6 \, pF$ are connected in series and a potential difference of $5000 \, V$ is applied across the combination. If the combination is disconnected and then reconnected in parallel, what will be the potential difference between the plates?

$A$ parallel plate capacitor has capacitance $C$. If the charges on the plates are $Q$ and $-3Q$,find the potential difference between the plates.

Two neutral conducting spheres of diameters $8 \ cm$ and $2 \ cm$ separated with a distance of $15 \ cm$ between their centres are joined by a thin conducting wire. $A$ charge of $100 \ nC$ is given to one of the spheres and the system is allowed to reach electrostatic equilibrium. The electric potential at a point on the line joining the centres of the two spheres where the net electric field becomes zero is . . . . . . $V$. (Neglect the charge acquired by the wire and $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \ Nm^2 C^{-2}$)