  In this paper, we have carried out linear and nonlinear analysis of tearing
and surface preserving modes of two dimensional (2D) Electron
Magnetohydrodynamics (EMHD). A linear analysis shows that the perturbations
parallel to equilibrium magnetic field $B_0$ (characteristic tangent hyperbolic
spatial profile), driven by the current gradients, lead to two different modes.
The first mode is the tearing mode having a non-local behavior which requires
the null-line in the magnetic field profile. Whereas, the second mode is a
surface preserving local mode which does not require the null-line in the
magnetic field. The quantity $B_0 - B_0^{''}$ should change sign for these
modes to exist. In nonlinear simulations, for tearing case we observe formation
of magnetic island at the null-line due to the reconnection of magnetic field
lines. However, for surface preserving mode, a channel like structure is
observed instead of the island structure.
