  Rutherford scattering formula plays an important role in plasma classical
transport. It is urgent to need a magnetized Rutherford scattering formula
since the magnetic field increases significantly in different fusion areas
(e.g. tokamak magnetic field, self-generated magnetic field, and compressed
magnetic field). The electron-ion Coulomb collisions perpendicular to the
external magnetic field are studied in this paper. The scattering angle is
defined according to the electron trajectory and asymptotic line (without
magnetic field). A magnetized Rutherford scattering formula is obtained
analytically under the weak magnetic field approximation. It is found that the
scattering angle decreases as external magnetic field increases. It is easy to
find the scattering angle decreasing significantly as incident distance, and
incident velocity increasing. It is shown that the theoretical results agree
well with numerical calculation by checking the dependence of scattering angle
on external magnetic field.
