  In the strong uniform magnetic field, the noncommutative plane (NCP) caused
by the lowest Landau level (LLL) effect, and QED with NCP (QED-NCP) are
studied. Being similar to the condensed matter theory of quantum Hall effect,
an effective filling factor $f(B)$ is introduced to character the possibility
that the electrons stay on the LLL. The analytic and numerical results of the
differential cross section for the process of backward Compton scattering in
the accelerator with unpolarized or polarized initial photons are calculated.
The existing data of BL38B2 in Spring-8 have been analyzed roughly and compared
with the numerical predictions primitively. We propose a precise measurement of
the differential cross sections of backward Compton scattering in a strong
perpendicular magnetic field, which may lead to reveal the effects of QED-NCP.
