  Magnetic fields and flows in coronal structures, for example, in gradual
phases in flares, can be described by 2D and 3D magnetohydrostatic (MHS) and
steady magnetohydrodynamic (MHD) equilibria. Within a physically simplified,
but exact mathematical model, we study the electric currents and corresponding
electric fields generated by shear flows. Starting from exact and analytically
calculated magnetic potential fields, we solveid the nonlinear MHD equations
self-consistently. By applying a magnetic shear flow and assuming a nonideal
MHD environment, we calculated an electric field via Faraday's law. The formal
solution for the electromagnetic field allowed us to compute an expression of
an effective resistivity similar to the collisionless Speiser resistivity. We
find that the electric field can be highly spatially structured, or in other
words, filamented. The electric field component parallel to the magnetic field
is the dominant component and is high where the resistivity has a maximum. The
electric field is a potential field, therefore, the highest energy gain of the
particles can be directly derived from the corresponding voltage. In our
example of a coronal post-flare scenario we obtain electron energies of tens of
keV, which are on the same order of magnitude as found observationally. This
energy serves as a source for heating and acceleration of particles.
