  We explore the two-dimensional motion of relativistic electrons when they are
trapped in magnetic fields having spatial power-law variation. Its impacts
include lifting of degeneracy that emerged in the case of the constant magnetic
field, special alignment of Landau levels of spin-up and spin-down electrons
depending on whether the magnetic field is increasing or decreasing from the
centre, splitting of Landau levels of electrons with zero angular momentum from
that of positive one and the change in the equation of state of matter. Landau
quantization (LQ) in variable magnetic fields has interdisciplinary
applications in a variety of disciplines ranging from condensed matter to
quantum information. As examples, we discuss the increase in quantum speed of
the electron in presence of spatially increasing magnetic field; and the
attainment of super Chandrasekhar mass of white dwarfs by taking into account
LQ and Lorentz force simultaneously.
