We have extended our variationally determined nonadiabatic polarization potential [Gibson and Morrison, Phys. Rev. A 29, 2497 (1984)] to the e-N2 system and calculated elastic, total momentum transfer, and rotational excitation cross sections. This model potential, which requires no scaling and contains no adjustable parameters, is presented in tabular and analytic (fitted) form for possible use in future studies. We evaluated the static potential at the near-Hartree-Fock level of accuracy and included exchange effects exactly via the linear algebraic method of Collins and Schneider [Phys. Rev. A 24, 2387 (1981)]. Diverse cross sections based on this model are in excellent agreement with existing experiment. We also compare various scattering quantities calculated with our model to prior theoretical results and to newly determined numbers using two other model potentials: a cutoff phenomenological form and the correlation-polarization potential of OConnell and Lane [Phys. Rev. A 27, 1893 (1983)].