Find the P.E. associated with a charge$\text{'}q\text{'}$ if it were present at the point $P$ with respect to the 'set-up' of two charged spheres, arranged as shown in figure below. Here $O$ is the mid-point of the line $O_1{O}_2$.

A sheet of aluminium foil of negligible thickness is placed between the plates of a capacitor, as shown in figure below. What effect has it on the capacitance if the foil is electrically insulated.

A sheet of aluminium foil of negligible thickness is placed between the plates of a capacitor, as shown in figure below. What effect has it on the capacitance if the foil is connected to the upper plate with a conducting wire?

The graph below shows the variation of voltage$V$ across the plates of two capacitors $A$ and $B$ versus increase of charge $Q$ stored on them. Which of the capacitors has higher capacitance? Give reason for your answer.

The given graph shows the variation of charge $q$ versus potential difference $V$ for two capacitors $C_1$ and $C_2$. The two capacitors have same plate separation but the plate area of $C_2$ is double than that of $C_1$. Which of the lines in the graph correspond to $C_1$ and $C_2$ and why?

As shown in the figure below, a dielectric material of dielectric constant $k$ is instead in half proportion between the plates of a parallel-plate capacitor. If its initial capacitance is $C$, what is the new capacitance?

Two identical capacitors of plate dimensions $l\times b$ and plate separation $d$ have dielectric slabs filled in between the space of the plates as shown in figures (a) and (b). Obtain the relation between the dielectric constants $k, k_1$ and $k_2$.

Find the capacitance of three parallel plates, each of area $\mathrm{A} {\mathrm{metre}}^2$ and separated by $d_1$ and $d_2$ metre. The in-between spaces are filled with dielectrics of relative permittivity ${\epsilon }_1$ and ${\epsilon }_2$. The permittivity of free space is ${\epsilon }_0$.

Figure below shows two capacitors joined in series, the rigid central section of length $b$ being movable. Prove that the equivalent capacitance of the combination is independent of the position of the central section.