On Beltrami fields with nonconstant proportionality factor on the plane

We consider the equation r o t B + α B = 0 on the plane with a being a real-valued function and show that it can be reduced to a Vekua equation of a special form. In the case when α depends on one Cartesian variable a complete system of exact solutions of the Vekua equation and hence of Eq. (1) is constructed basing on Bersʹ theory of pseudoanalytic formal powers.