The complete electron-nucleus cross section, containing both longitudinal and transverse interactions, has been obtained for elastic as well as inelastic scattering using the eikonal wave functions of Yennie et al. This approach is based on the distorted-wave Born approximation, and retains only the leading term in an asymptotic expansion (in inverse powers of momentum transfer times nuclear radius) of the eikonal integrals. The method should be valid at electron energies above 2-300 MeV, and should constitute an improvement over the phase-shift method when the latter becomes inaccurate above 4-500 MeV. A simple collective nuclear model for magnetic transitions is also given, which contains the rotational collective flow of nuclear charge.NUCLEAR REACTIONS Electron scattering $^{27}\mathrm{Al}$, $^{51}\mathrm{V}$, $^{115}\mathrm{In}$, $^{208}\mathrm{Pb}$, $^{209}\mathrm{Bi}$ calculated elastic, inelastic magnetic form factors using eikonal method.