[en] The effect of an externally applied high-frequency oscillating electric field on the critical nucleation field of superconductivity in the bulk as well as at the surface of a superconductor is investigated in detail in this work. Starting from the linearized time-dependent Ginzburg-Landau (TDLG) theory, and using the variational principle, I have shown the analogy between a quantum harmonic oscillator with that of the nucleation of superconductivity in the bulk and a quantum double oscillator with that of the nucleation at the surface of a finite sample. The effective Hamiltonian approach of Cook et al (1985 Phys. Rev. A 31 564) is employed to incorporate the effect of an externally applied highly oscillating electric field. The critical nucleation field ratio is also calculated from the ground state energy method. The results obtained from these two approximate theories agree very well with the exact results for the case of an undriven system, which establishes the validity of these two approximate theories. It is observed that the highly oscillating electric field actually increases the bulk critical nucleation field (H_c2) as well as the surface critical nucleation field (H_c3) of superconductivity as compared to the case of absent electric field (ε₀ = 0). But the externally applied rapidly oscillating electric field accentuates the surface critical nucleation field more than the bulk critical nucleation field, i.e. the increase of H_c3 is 1.6592 times larger than that of H_c2