We study the effect of the external magnetic field on the scattering o
f an electron off a free hadron in the ultrarelativistic limit of elec
trons. In this work, the electrons are specifically assumed to he init
ially in their lowest Landau level. Our calculations show that the cro
ss sections seriously depend on the external magnetic field for the fi
xed initial electron energy, As the magnetic field strength increases,
above some critical value B-c, the cross section of electron-neutron
scattering increases continuously, while that of electron-proton scatt
ering becomes constant. Both of them decrease drastically as the magne
tic field strength decreases below B-c.