

Conductors in electrostatic field § 1 of the The charge distribution in the conductor. The connection between the field intensity at the surface of the conductor and the surface charge density
Free charges in the conductor can move under the influence of an arbitrarily small force. Therefore, for the balance of the charges in the conductor must meet the following conditions:
Consequently, the surface charge of the conductor at equilibrium is an equipotential. Consider a closed surface in the form of a cylinder whose generators are perpendicular to the surface of the conductor. On the surface of the conductor are free charges with surface density σ. Because inside a conductor there are no charges, the flow through the surface of the cylinder inside the conductor is zero. The flow through the top of the cylinder outside the a conductor on the Gauss theorem is equal
ie electric displacement vector equal to the surface density of free charges of a conductor or
II. In making an uncharged conductor to an external electrostatic field his free charges will move: positive  on the field, negative  against the field. Then on one side of the conductor will accumulate positive and the other negative charges. These charges are said to be induced. The redistribution of the charges will be as long as the intensity in the conductor becomes zero, and the line intensity outside of the conductor will be the perpendicular to the surface. Induced charges appear on the conductor due to the displacement, ie are surface density charges and shifted as is therefore called the electric displacement vector.
§ 2 Capacitance conductors. Capacitors I. Secluded called conductors, far from other conductors bodies charges. The potential of such a conductor is directly proportional to the charge on it
From experience, it follows that different conductors, being equally charged Q_{1} = Q_{2} takes various potentials φ_{1} ≠φ_{2} due to the different shapes, sizes, and surrounding environment conductor (ε). Therefore, for an isolated conductor have the formula , where  capacity of secluded conductor. Capacity of the secluded conductor is equal to a charge q, give the conductor that changes its potential by 1 volt.
In the SI system capacity is measured in farads
Capacity of the ball
Calculate the capacity of parallelplate capacitor with plates of area S, the surface charge density σ, the dielectric constant ε of the dielectric between the plates, the distance between the plates is d. The field intensity is . Using the relation Δφ and E, we find

capacity of plate capacitor For a cylindrical capacitor:
For a spherical capacitor:
Because for some values ??of the voltage in the dielectric breakdown occurs (electrical discharge through the dielectric layer), then there is a breakdown voltage capacitors. Breakdown voltage depends on the shape of facings, dielectric properties and its thickness.
According to the law of conservation of charge
b) serial connection
According to the law of conservation of charge
§ 3 The energy of the electrostatic field
The electrostatic field is potential. The forces acting between charges  conservative forces. System of fixed point charges should have potential energy. We find the potential energy of two fixed point charges q_{1} and q_{2}, separated by a distance r from each other. The potential energy of the charge q_{2} in the field created charge q_{1}, equal to
Similarly, the potential energy of the charge q_{1} in the field created by a charge q_{2}, equal to
It is seen that W_{1} = W_{2}, then identify potential energy of the system of charges q_{1} and q_{2} in W, we can write
where φ_{i}  potential generated at the point where the charge q_{i}, all charges except the ith.
The energy of the electric field of a charged secluded conductor can be determined by considering the total work done on the movement of small amounts of charge dq from infinity to this conductor. If the conductor has a charge q, capacitance C and potential φ, is to transfer the charge dq from infinity to conductor the work must be expended
To charge conductor from ground potential to a potential φ must do the work
The potential energy equal to the work that needs to be performed in order to charge the conductor
4. The energy of a charged capacitor. We express the energy of the capacitor through the values ??characterizing the capacitor
because field is uniform inside the capacitor, you can enter the volume energy density (bulk density  the energy per unit volume)
