What is the net force on a small electric dipole placed inside a parallel plate capacitor at steady state,if the plates are separated by $1 \ cm$? The circuit diagram is provided.

The resultant capacitance between $A$ and $B$ in the figure is ...... $\mu F$.

$A$ 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.

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)

Two metal spheres,one of radius $R$ and the other of radius $2R$,both have the same surface charge density $\sigma$. They are brought in contact and then separated. What will be the new surface charge densities on them?

The diagram shows four capacitors with capacitances and breakdown voltages as mentioned. What should be the maximum value of the external emf source such that no capacitor breaks down? (in $kV$)