VECTOR SOLUTIONS OF THE LAPLACE EQUATION AND THE INFLUENCE OF HELICITY ON THE AHARONOV-BOHM SCATTERING

Vector solutions of the Laplace equation are obtained. Their propertie s and possible applications are discussed. The multipole toroidal mome nts appear naturally in this vector basis. This removes the mystery of their origin. Conditions are found for the non-radiation of charge an d current densities periodically changing with time. Electromagnetic p roperties of the toroidal solenoid with non-zero helicity, the influen ce of the latter on the Aharonov-Bohm scattering and alternative viewp oint on the toroidal solenoid with nontrivial helicity are studied.