Three uncharged capacitors of capacitance $C_1,C_2$, and $C_3$ are connected as shown in Fig. to one another and to points $A,B$, and $D$ at potentials ${\varphi }_A, {\varphi }_B$, and ${\varphi }_D$. Determine the potential ${\varphi }_0$ at point $O$.

The thickness of a flat sheet of a metal foil is $d$, and its area is $S$. A charge $q$ is located at a distance $l$ from the centre of the sheet such that $d\ll V\overline{S}\ll l$

Determine the force $F$ with which the sheet is attracted to the charge $q$, assuming that the straight line connecting the charge to the centre of the sheet is perpendicular to the surface of the sheet.

Where must a current source be connected to the circuit shown in the figure, in order to charge all the six capacitors having equal capacitances?

A parallel-plate capacitor is filled by a dielectric whose permittivity varies with the applied voltage according to the law $\epsilon =\alpha U$, where $\alpha =1{ \mathrm{V}}^{-1}$. The same (but containing no dielectric) capacitor charged to a voltage $U_0=156 \mathrm{V}$ is connected in parallel to the first "nonlinear" uncharged capacitor. Determine the final voltage $U$ across the capacitors.

Two small balls of mass $m$, bearing a charge $q$ each, are connected by a nonconducting thread of length $2l$. At a certain instant, the middle of the thread starts moving at a constant velocity $v$ perpendicular to the direction of the thread at the initial instant. Determine the minimum distance $d$ between the balls, 

Two balls of charge $q_1$ and $q_2$ initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by $60°$, and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by $90°$.

In what proportion will the velocity of the second ball change? Determine the magnitude of the charge-to-mass ratio for the second ball if it is equal to $k_1$ for the first ball. The electrostatic interaction between the balls should be neglected. 

Why do electrons and not ions cause collision ionization of atoms, although both charges acquire the same kinetic energy $\frac{m{v}^2}{2}=e\Delta \varphi$ ( $e$ is the charge of the particles, and $\Delta \varphi$ is the potential difference) in an accelerating field? Assume that an atom to be ionized and a particle impinging on it have approximately the same velocity after the collision.

Two small identical balls lying on a horizontal plane are connected by a weightless spring. One ball is fixed at point, $O$ and the other is free. The balls are charged identically, as a result of which the spring length increases twofold. Determine the change in the frequency of harmonic vibrations of the system.