Talking about what the energy of the electric field, it should be pointed out that this is the most important parameters.Despite the fact that the term "energy" is quite familiar and seemingly obvious, in this case, you need a good understanding of what is at stake.For example, as is known, the energy of the electric field can be measured at any arbitrary level it, conventionally taken as the origin (that is, zero).Although it gives some flexibility in preparing the calculation, an error could lead to a very different computing power.This time we will clarify later, using the formula.
electric field energy is directly related to the interaction of two or more point charges.Consider the example of two charges - q1 and q2.The potential energy of the electric field (in this case - electrostatics) is defined as:
W = (1/4 * Pi * E0) / (q1 * q2 / r),
where E0 - tension, r - distance between charges, Pi - 3.141.
Since the field of the first acts on the second (and vice versa), then we define the potential of these fields.The first charge has an impact on the second:
W = 0.5 * (q1 * Fi1 + q2 * Fi2).
In this formula (denoted by 1) has two new quantities - Fi1 and Fi2.We calculate them.
Fi1 = (1/4 * Pi * E0) / (q2 / r).Accordingly
:
Fi2 = (1/4 * Pi * E0) / (q1 / r).
Now the first important point: the formula "1" contains two terms (q * Fi), actually represents the energy of interaction between charges and a factor of 0.5.However, the energy of the electric field - is not part of any charge, therefore, to take account of this feature, it is necessary to introduce a correction "0.5."
As already mentioned, the interaction have on each other several charges (not necessarily just two).In this case, the energy density of the electric field above.Its value can be found by summing the data obtained for each pair.
Now back to the issue of the choice of the reference mentioned in the beginning of this article.Thus, from the formulas that if the calculation is carried out with respect to any points, the distance from the charge which tends to infinity, then the result is the value of work that will make a field different charges from each other at an infinite distance.But if you must know the value of the field work spent on a relatively small movement of the charges themselves, the starting point can be chosen either as a result of calculations obtained value does not depend on the choice of the reference point.
give an example of how it can be used in practical calculations.For example, there are three of the charge, the spatial configuration of which is a triangle.Distance (r) between q1, q2 and q3 are equal.
calculate potential:
Fi = 2 * (q / 4 * Pi * E0 * r).
can now determine the energy of interaction between charges themselves:
W0 = 3 * ((q * q) / 4 * 3.141 * E0 * r).
It is this work that will be made when moving to an infinite distance.
If all three shift occurs from the common center of the same amount, the triangle formed with sides r1 (against the previous r).
define energy:
W = 3 * ((q * q) / 4 * Pi * E0 * r1).
In this case, we can talk about reducing the overall energy value of all three charges.It should be noted that if the value r1 (r) tends to infinity, the original energy and produced the work becomes.
complicate the problem and removed from the system one arbitrary charge.The result is a classic case of two charges located at a distance r.
energy of such a system is:
W = (q * q) / (4 * Pi * E0 * r).
and the field itself will perform the work on the movement of numerically equal to:
A = 2 * ((q * q) / 4 * Pi * E0 * r).
Then everything is simple: the removal of yet another charge lead to the fact that the total energy is equal to zero (no distance).In this work, and the field is numerically equalized.In other words, the original energy is completely converted into work.
The calculations associated with determining the energy of the electric field, as a rule, are used for the selection of capacitors.After each such device consists of two plates separated by a distance r, at each of which the charge is concentrated.
