The main objective of the section of electrostatics formulated as follows: for a given distribution in space and the amount of electric charge (field source) to determine the value of the intensity vector E at all points of the field.The solution to this problem is possible on the basis of such a thing as the principle of superposition of the electric fields (principle of independence of action of the electric field) intensity of any of the electric field of the charge will be equal to the geometric sum of the field strengths, which are created by each of the charges.
charge generated electrostatic field can be divided in space or diskertno or continuously.In the first case, the field strength:
n
E = Σ Ei₃
i = t,
where Ei - tension in a particular point in space field created by one i-th charge system, and n - the total number of diskertnyh charges thatincluded in the system.
example of solving the problem, which is based on the principle of superposition of electric fields.So to determine the strength of the electrostatic field that is created in a vacuum stationary point charges q₁, q₂, ..., qn, use the formula:
n
E = (1 / 4πε₀) Σ (qi / r³i) ri
i =t,
where ri - the radius vector drawn from the point charge of qi in a given point of the field.
give another example.Determination of the electrostatic field that is created in a vacuum electric dipole.
electric dipoles - a system of two identical in absolute value and, thus, opposite charges q & gt; 0 and -q, the distance I between which are relatively small compared with the distance of the points under consideration.Shoulder dipole will be called the vector l, which is directed along the axis of the dipole to the positive charge from the negative and numerically equal to the distance I between them.Vector pₑ = ql - electrical dipole moment (electric dipole moment).
voltage E dipole field at any point:
E = + E₊ E₋,
where E₊ and E₋ are field strengths of electric charges q and -q.
Thus, at point A, which is located on the axis of the dipole strength of the dipole field in a vacuum is equal
E = (1 / 4πε₀) (2pₑ / r³)
At point B, which is located on the perpendicular, restored to the axisdipole from its middle:
E = (1 / 4πε₀) (pₑ / r³)
At an arbitrary point M, quite remote from the dipole (r≥l), a module of its field strength is
E = (1 / 4πε₀)(pₑ / r³) √3cosθ + 1
In addition, the principle of superposition of the electric fields consists of two statements:
- Coulomb force of interaction of two charges is not dependent on the presence of other charged bodies.
- Assume that the charge q interacts with the system charges q1, q2,..., Qn.If each of the charges of the system acts on the charge q with a force F₁, F₂, ..., Fn, respectively, the resultant force F, applied to the charge q on the part of the system is equal to the vector sum of the separate forces:
F = F₁ + F₂ + ... + Fn.
Thus, the principle of superposition of electric fields allows to come to an important statement.
As you know, the law of gravity is valid not only for point masses, but also for balls with a spherically symmetric distribution of mass (in particular for the ball and a point mass);Then r - the distance between the centers of the balls (from the point mass to the center of the ball).This follows from the mathematical form of the law of universal gravitation and the principle of superposition.
Since the formula of Coulomb's law has the same structure as the law of gravitation, and the Coulomb force and made the principle of superposition of fields, it is possible to make a similar conclusion: Coulomb will work together two loaded ball (point charge with the ball), provided thatballs are spherically symmetric charge distribution;the value of r in this case is the distance between the centers of the balls (from a point of charge to the ball).
That is why the field strength of a charged ball is out of the ball is the same as that of a point charge.
But in electrostatics, unlike gravity, with a term such as a superposition of fields, we must be careful.For example, when approaching positively charged metal balls spherical symmetry is broken: the positive charges, mutually pushing, will tend to the most remote from each other sections of the balls (the centers of positive charges will be farther apart than the centers of the balls).Therefore, the repulsive force of balls in this case will be less than the value that is derived from Coulomb's law by substituting instead of r the distance between the centers.
