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The elements of dielectric tensor and dispersion relation for obliquely propagating whistler waves with finite k⊥ in an infinite magnetoplasma are obtained for a kappa distribution in the presence of perpendicular a.c. electric field. Integrals and modified plasma dispersion functions are reduced in power series form. Numerical calculations have been performed to obtain temporal growth rate and real frequencies of the plasma waves for magnetospheric plasma, using linear theory of dispersion relation. The effect and modification introduced by the perpendicular a.c. electric field on the temporal growth rates, real frequencies and resonance condition are discussed for kappa and Maxwellian distributions. Our results and their interpretation are compared with known whistler observations obtained by ground-based techniques and satellite observations.