Speaking about what is the energy of an electric field, one cannot but indicate that this is its most important parameter. Despite the fact that the term “energy” itself is quite familiar and, at first glance, obvious, in this case you need to understand well what is being discussed. For example, as you know, the energy of an electric field can be measured from any arbitrary level, conditionally taken as the reference point (that is, for zero). Although this gives some flexibility in the preparation of calculations, the error can lead to calculations of a completely different energy. This moment we will clarify a little later, using the formula.
The energy of the electric field is directly related to the interaction of two or more point charges. Consider an example with two charges - q1 and q2. The potential energy of an electric field (in this case, electrostatics) is defined as:
W = (1/4 * Pi * E0) / (q1 * q2 / r),
where E0 is the intensity, r is the distance between charges, Pi is 3.141.
Since the field of the first acts on the second (and vice versa), we determine the potentials of these fields. The first charge affects the second:
W = 0.5 * (q1 * Fi1 + q2 * Fi2).
In this formula (we denote it 1) there are two new quantities - Fi1 and Fi2. We calculate them.
Fi1 = (1/4 * Pi * E0) / (q2 / r).
Respectively:
Fi2 = (1/4 * Pi * E0) / (q1 / r).
Now the first important point: formula “1” contains two terms (q * Fi), which in fact are the energy of interaction of charges and a coefficient of 0.5. However, the energy of the electric field is not part of any charge, therefore, in order to take this feature into account, the correction “0.5” must be introduced.
As already indicated, several charges exert an interaction on each other (not necessarily just two). In this case, the energy density of the electric field is higher. Its value can be found by summing the data obtained for each pair.
Now back to the problem of choosing the origin mentioned at the beginning of the article. Thus, it follows from the formulas that if the calculations are carried out with respect to arbitrary points, the distance from the charges of which tends to infinity, the result will be the value of the work that the field will perform, carrying the charges apart from each other to an infinite distance. But if it is necessary to find out the value of the work of the field spent on a relatively small movement of the charges themselves, then the reference point can be chosen any, since the value obtained as a result of the calculations does not depend on the choice of the reference point.
We give an example of how this can be used in practical calculations. For example, there are three charges whose spatial configuration is a triangle. The distances (r) between q1, q2 and q3 are equal.
Calculate the potential:
Fi = 2 * (q / 4 * Pi * E0 * r).
Now you can determine the interaction energy of the charges themselves:
W0 = 3 * ((q * q) / 4 * 3.141 * E0 * r).
This is exactly the work that will be accomplished when moving to an infinite distance.
If the displacement of all three occurs from the common center by the same amount, a triangle is formed with sides r1 (against the previous r).
Determine the energy:
W = 3 * ((q * q) / 4 * Pi * E0 * r1).
In this case, we can talk about a decrease in the total energy of the entire system of three charges. It is worth noting that if the quantity r1 (r) tends to infinity, then the initial energy and the work performed become equal.
We complicate the task and remove one arbitrary charge from the system. As a result, we obtain the classical case with two charges located at a distance r.
The energy of such a system is equal to:
W = (q * q) / (4 * Pi * E0 * r).
And the field itself will perform the work of displacement, numerically equal to:
A = 2 * ((q * q) / 4 * Pi * E0 * r).
Then everything is simple: the removal of another charge will lead to the fact that the total energy becomes equal to zero (there is no distance). In this case, the work and the field are numerically equalized. In other words, the original energy is completely transformed into work.
Calculations associated with determining the energy for an electric field are usually used to select capacitors. Indeed, each such device consists of two plates separated by a distance r, on each of which the charge is concentrated.