∂ $^{i}$Bk e − ∂ $^{k}$Bi e ≡ F ik B$_{e}$ = F ⋆ ik A$_{e}$ = 1 2 e $^{iklm}$F$_{A}$$_{e}$$_{lm}$ . (28) Using the effective potential, we replace in equations the external electromagnetic field generated by magnetic (electrical) charges, which affects an electrical (magnetic) charge, by the same electromagnetic field generated by fictitious electrical (magnetic) charges; the necessary requirement for such replacement is that magnetic (electrical) charges j i µ ( x ) ≡ 0 [ j i $_{e}$( x ) ≡ 0, respectively] must be absent in the space-time region of interest. Because we do not consider particles bearing both electrical and magnetic charges, this requirement is always met locally, in the close vicinity of electrical (magnetic) charge. We use the variational principle to derive Lagrange-Euler differential equations (i.e. we derive them locally), hence, we may assume that the requirement above is met. The introduction of effective potentials in some space-time region is possible for the con- figurations of electrical E and magnetic H fields, which may be generated both by electrical and magnetic charges, not present in the region of interest. Such configurations of elec- tromagnetic field may be called free (independent of the type of charges) configurations. Electromagnetic waves, by which means the interaction of charged particles is performed, are examples of free configurations. If the necessary requirement is met, the force lines of an external electromagnetic field within a quite small space-time region are close to recti- linear, while the electromagnet field’s configurations close to rectilinear may be, apparently, generated by currents of both electrical and magnetic charges, not present in the region of interest, i.e. the configurations of any electromagnetic field in the space-time region with no electrical and magnetic charges are locally free. Therefore, the effective potentials are (locally) defined in a correct way. According to the definition, effective vector-potential A i µ depends on partial derivatives ∂ $^{l}$Bm µ ; similarly, effective pseodovector-potential B i e depends on partial derivatives ∂ $^{l}$Am e . Consideration of the dependence of A i µ on partial derivatives ∂ $^{l}$Bm µ with a varying B$_{µ}$ would lead to the occurrence of a term linearly depending on the value of current density j$_{e}$ in the right-hand part of equation (15b) (for example, a partial case of a constant electromagnetic field may be considered, in this case the effective vector-potential A$_{µ}$ can be easily expressed via tensor F$_{B}$$_{µ}$ : however, in general case, the dependence of A i µ on partial derivatives ∂ $^{l}$Bm µ is not trivial) A i µ = − 1 2 F ik $_{A$_{µ}$}$x$_{k}$ = − 1 4 e $^{iklm}$F$_{B}$$_{µ}$$_{lm}$ x$_{k}$ ; (29) 8