  The 2-dimensional charge transport with parallel (in plane) magnetic field is
considered from the physical and mathematical point of view. To this end, we
start with the magnetic field parallel to the plane of charge transport, in
sharp contrast to the configuration described by the theorems of Aharonov and
Casher where the magnetic field is perpendicular. We explicitly show that the
specific form of the arising equation enforce the respective field solution to
fulfil the Majorana condition. Consequently, as soon any physical system is
represented by this equation, the rise of fields with Majorana type behaviour
is immediately explained and predicted. In addition, there exists a quantized
particular phase that removes the action of the vector potential producing
interesting effects. Such new effects are able to explain due the geometrical
framework introduced, several phenomenological results recently obtained in the
area of spintronics and quantum electronic devices. The quantum ring as spin
filter is worked out in this framework and also the case of the quantum Hall
effect.
