$A$ 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.

$A$ parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to a potential $V$ and then the battery is disconnected. $A$ slab of dielectric constant $k$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q$,$E$,and $W$ denote respectively the magnitude of charge on each plate,the electric field between the plates (after the slab is inserted),and the work done on the system in the process of inserting the slab,then state the incorrect relation from the following:

Two identical charged spherical drops,each at a potential $V$,coalesce to form a single larger drop. If the capacitance of each small drop is $C$,find the potential of the larger drop.

$A$ 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 $(\epsilon_{0} = \text{permittivity of free space})$

The distance between the plates of a parallel plate capacitor is $5d$. The positively charged plate is at $x=0$ and the negatively charged plate is at $x=5d$. Two slabs,one of a conductor and the other of a dielectric,both of equal thickness $d$,are inserted between the plates as shown in the figure. The potential versus distance graph will look like:

$64$ identical mercury drops,each charged to a potential of $10\, V$,are combined to form a single larger drop. The potential of the new larger drop is........$V$.