The field picture near the wires with current (Картина поля вблизи провода с током)

That’s the general picture which corresponds to the transmission line with arbitrary load. Due to the presence of a small tangential component of the electric field strength vector at the surface of the conductor with current, the resulting electric field strength vector E is not perpendicular to the surface of the conductor. This leads to the appearance of the normal component of the Poynting vector at the surface of the conductor. Consequently part of the transmitted energy is absorb inside the wires of the transmission line.

There are two wires which carry current to the load and from the load. Certainly, there should be a voltage between these two wires that’s why that’s a line which shows the electric field in the space around these wires. The normal component of the electric field corresponds to the voltage between wires that’s the voltage as if two lines form a capacitor. But also, there is a horizontal component which corresponds to the Ohm's Law, in such a case the Poynting’s vector will come just inside the wire, partly, the energy is transformed from the source to the load, and the horizontal part of the Poynting’s vector just illustrate this energy, transformed from the source to the load. But the small vertical component of the Poynting’s vector illustrates the power, which is dissipated in non-ideal wires. If the wires are ideal than there should not be component of the Poynting’s vector which will come inside the wire. All these S-vectors will be parallel to the wire surface. H here in any case is induced by the current inside wire and the H-field, magnetic field, circulates around the wires, H-vector has no component which is directed from the power source to the load, this vector is always normal to our surface.

25. Energy flows in static electric and magnetic fields (Поток энергии в статических электрических и магнитных полях).

W e 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.