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In the present work, it is shown that, the application of the Bazanskiapproach to Lagrangians, written in AP-geometry and including the basic vectorof the space, gives rise to a new class of path equations. The general equationrepresenting this class contains four extra terms, whose vanishing reduces thisequation to the geodesic one. If the basic vector of the  AP-geometry is considered as playing the role of the electromagneticpotential, as done in a previous work, then the second term  (of the extra terms) will represent Lorentz force while the fourth term givesa direct effect of the electromagnetic potential on the motion of the chargedparticle. This last term may give rise to an effect similar to theAharanov-Bohm effect. It is to be considered that all extra terms will vanishif the space-time used is torsion-less.Comment: 11 pages, LaTeX fil

A NEW CLASS OF PATH EQUATIONS IN AP-GEOMETRY