  We consider the electron magnetohydrodynamics (MHD) with static background
ion flow. A special situation of $B(x,y,t)=\nabla\times (a\vec e_z)+b \vec e_z$
with scalar-valued functions $a(x,y,t)$ and $b(x,y,t)$ was studied numerically
in the physics paper [7]. The authors concluded from numerical simulations that
there is no evidence of dissipation cutoff for the electron MHD. In this paper
we show the existence of determining wavenumber for the electron MHD, and
establish a regularity condition only on the low modes of the solution. Our
results suggest that the conclusion of the physics paper on the dissipation
cutoff for the electron MHD is debatable.
