A cylindrical capacitor is filled with two cylindrical layers of dielectric with permittivities ${\epsilon }_1$ and ${\epsilon }_2.$ The inside radii of the layers are equal to $R_1$ and $R_2 \left(R_2>R_1\right)$. The maximum permissible values of electric field strength are equal to $E_{1\mathrm{m}}$ and $E_{2\mathrm{m}}$, for these dielectrics. At what relationship between ${\epsilon }_1{R}_1$ and $E_{\mathrm{m}}$, will the voltage increase result in the field strength reaching the breakdown value, for both dielectrics simultaneously?

Two long straight wires with equal cross-sectional radii $a$ are located parallel to each other in air. The distance between their axes equals $b$. Find the mutual capacitance of the wires per unit length, under the condition $b\gg a$.

Find the capacitance of a system of identical capacitors between points $A$ and $B$, as shown in the figures.
(a)
(b)

Four identical metal plates are located in air at equal distances $d$ from one another. The area of each plate is equal to $S$. Find the capacitance of the system between points $A$ and $B$, if the plates are interconnected as shown.
(a) 
(b)

Find the capacitance of an infinite circuit formed by the repetition of the same link, consisting of two identical capacitors each with capacitance $C$ (figure).

In the circuit shown in the figure, the emf of each battery is equal to $\epsilon =60 \mathrm{V}$ and the capacitor capacitance equals $C_1=2.0 \mathrm{\mu F}$ and $C_2=3.0 \mathrm{\mu F}$. Find the charges which will flow after the shorting of the switch $Sw$, through sections $1, 2$ and $3$, in the directions indicated by the arrows?

Determine the interaction energy of the point charges located at the corners of a square with the side $a$, in the circuits shown in the figures.