SELF

16

S.B. Karavashkin and O.N. Karavashkina

3. Pattern of space and time distribution of dynamic electric field potential

With the help of above described simple method of deformed grid, let us plot the diagram of distribution of potential of dynamic electric dipole in the plane running along the dipole axis. For it, we need to know the equation of dynamic potential of this dipole. In its turn, to find this equation, we will use the principle of additivity of the field potential created by several charges.

"To determine the energy of system n of point charges e_i (i = 1, 2, 3, ..., n) , we probably have to write down for each pair of these charges the expressions like

(where W is the energy of interaction of charges e₁  and e₂, R₁₂ is the distance between the charges, _i is the potential of the charge e₂ at the point of location of the charge e₁) or

and add all these expressions. Gathering all terms of the sum which have e_k as the multiplier, we will make sure that the coefficient at the e_k which we will denote as _k/2   will be equal to

The expression in the brackets is, probably, the value of potential of the whole system of charges at the point of location of the charge e_k or, rather, the potential of the whole system of charges, except the charge e_k (the potential _k,k   of the charge e_k at the point of field where it is located is not included to the expression for _k , and it basically has not a physical meaning, as turns to infinity). Thus, the mutual energy of the system of n charges is equal to

where _k  is the potential at the point of location of the charge e_k" [3, p. 80].

Taking now e_k  as the trial charge, we in accordance with (10) come to the condition of additivity, which allows us to represent the field as the sum of fields created by each charge of multipole separately. This principle will remain also at the transition to dynamic fields, only in addition to the spatial parameters in (10) we have to take into account the phase delay arising when different distances from the field sources to the studied point; we will speak of this later.

The next our step to find the modelling equation of scalar potential would be, as usually, to introduce the correlation between the oscillating charge and dipole. This is the following well known correlation [4, p. 434]:

However we may not use this analogy, because, as we showed in [1], in case of moving source the field considerable transforms, which has great effect on the field pattern in the near field.