Energy flows in static fields (Поток энергии в статических полях)

We can create a system where both electric and magnetic field are constant and the same they are normal to each other. Formally, the Poynting vector can also be applied to static electric and magnetic fields. As an example, we can consider a cylindrical capacitor in a homogeneous magnetic field.

These two dashed (пунктир) areas are the poles of the magnet. So, this is magnet and magnetic field, which is shown here like vertical lines. The magnetic field is uniform, everywhere has the same volume, magnitude and has only one component – vertical. Now electric field, there is a cylindrical capacitor, the central electrode is charged, and this outer electrode is charged to the same charge but another potential. That’s why there is a potential difference between central electrode and outer electrode. In such a case an electric field will be induced, and we shall consider that this E (electric field) has only horizontal direction. Now, electric and magnetic fields in every point inside the capacitor will be normally directed, the direction between them will be equal to 90°. Before we have seen if electric and magnetic field has such directions they produce the Poynting vector (energy flow vector). If we shall formally use this assumption than we can say – there should be energy flow and we could calculate this energy flow using formal rules. .

(What this formula shows? It is the cylindrical capacitor, in the cylindrical capacitor the electric field depends on the radius, propotional to the radius). This is just an expression which corresponds to the electric field, it has inverse proportional to the radius, if we shall move from the central wire, we see that the electrical field will be less and less. Here is the form r (radius) over r squared it is done to tip this vector product. Nevertheless it is interesting that we have found out there will be a flow of the energy this brackets not only the magnitude but for understanding what will be the direction of energy flow. This Poynting's vector should be normal to the H-vector and radius, if we shall at the system from the another direction (from the up part) we will see that this energy flow will circulate around the central electrode in the space of the capacitor.

The momentum of the electromagnetic field (Момент электромагнитного поля)

The electromagnetic field inside the cylinder has some mass, as a consequence of the Einstein theorem, the mass of the any kind of a material may be expressed in terms of its energy. Now let’s consider some general relations.

Delta p is equal to m effective time v. That is the momentum mass and velocity. If the electromagnetic field induces the Poynting vector and the energy start to circulate somewhere it should circulate with the velocity v, because it is velocity of a propagation of the electromagnetic energy. Effective mass, what is it? Let’s assume that the electromagnetic field inside this cylindrical capacitor have some mass that means that it has some density, if we shall multiply density and volume of the vacuum inside the capacitor than we shall get a total mass, which is enclosed inside this capacitor.

It is some cylinder where something is propagated, so the velocity corresponds to the distance which passes the electromagnetic wave at the velocity of c. The S-energy which passes the area times s (the total energy which crosses the distance between the inner electrode and external electrode).

It should be equal to the effective mass times v, because they are the same, effective mass of the electromagnetic field, that is the moment of the electromagnetic field. How to calculate the energy of the electromagnetic field?