  We present a systematic approach for the separation of variables for the
two-dimensional Dirac equation in polar coordinates. The three vector
potential, which couple to the Dirac spinor via minimal coupling, along with
the scalar potential are chosen to have angular dependence which emanate the
Dirac equation to complete separation of variables. Exact solutions are
obtained for a class of solvable potentials along with their relativistic
spinor wavefunctions. Particular attention is paid to the situation where the
potentials are confined to a quantum dot region and are of scalar, vector and
pseudo-scalar type. The study of a single charged impurity embedded in a 2D
Dirac equation in the presence of a uniform magnetic field was treated as a
particular case of our general study.
