Abstract
It is shown that a relativistic spin-1/2 neutral particle with an anomalous magnetic moment moving in an x-y plane in a two-dimensional electrostatic field: E=(Ex(x, y), Ey(x, y), O) has (N-1)-fold degeneracy of the ground state. The degree of degeneracy of the ground state is defined by the value of the anomalous magnetic moment and a linear charge density of the filament creating this electrostatic field.