The dispersion relation for the whistler mode instability in an infinite bi-Maxwellian magnetoplasma in the presence of a parallel ac electric field has been derived using the method of characteristic solutions. The perturbed and unperturbed particle trajectories have been used to determine the perturbed distribution function. The growth rate has been determined. The earlier known results are recovered under suitable approximations, when the ac field amplitude and frequency are set to zero. It is found that the ac field parameters modify the growth rate and the resonance, condition of the charged particles. The growth rate for various frequencies and magnitudes of the ac field, suitable to magnetospheric conditions, has been evaluated. It has been found that the growth rate depends significantly on the variation of the frequency rather than on the variation of the magnitude. ¿ American Geophysical Union 1993