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?

Find the potential difference ${\mathrm{\phi }}_{\mathrm{A}}-{\mathrm{\phi }}_{\mathrm{B}}$ between points $A$ and $B$, of the circuit shown in figure.

Determine the potential at point $1$, at point $2$ and at point $3$, of the circuit shown in the figure, assuming the potential at the point $O$ to be equal to zero.

Find the capacitance of the circuit shown between points $A$ and $B$.

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.

There is an infinite straight chain of alternating charges $q$ and $-q$. The distance between the neighbouring charges is equal to $a$. Find the interaction energy of each charge with all the others. Instruction: Make use of the expansion of $\ln (1+\alpha )$ in a power series in $\alpha$.

A point charge $q$ is located at a distance $l$ from an infinite conducting plane. Find the interaction energy of that charge with those induced on the plane.

Calculate the interaction energy of two balls, whose charges $q_1$and $q_2$ are spherically symmetrical. The distance between the centres of the balls is equal to $l$.

Instruction: Start with finding the interaction energy of a ball and a thin spherical layer.