  The effect of an exponentially decaying magnetic field on the dynamics of
Dirac fermions in 3+1 dimensions is explored. The spatially decaying magnetic
field is assumed to be aligned in the third direction, and is defined by
{\mathbf{B}}(x)=B(x){\mathbf{e}}_{z}, with B(x)=B_{0}e^{-\xi\ x/\ell_{B}}.
Here, \xi\ is a dimensionless damping factor and \ell_{B}=(eB_{0})^{-1/2} is
the magnetic length. As it turns out, the energy spectrum of fermions in this
inhomogeneous magnetic field can be analytically determined using the Ritus
method. Assuming the magnetic field to be strong, the chiral condensate and the
\textit{local} electric current correlation function are computed in the lowest
Landau level (LLL) approximation and the results are compared with those
arising from a strong homogeneous magnetic field. Although the constant
magnetic field B_{0} can be reproduced by taking the limit of \xi-> 0 and/or
x-> 0 from B(x), these limits turn out to be singular once the quantum
corrections are taken into account.
