The effect of cold plasma beam on electromagnetic whistler wave with perpendicular AC electric field has been studied by using the unperturbed Lorentzian (Kappa) distribution in the Earth's atmosphere for relativistic plasma. The cold plasma has been described by a simple Maxwellian distribution where as Lorentzian (Kappa) distribution function has been derived for relativistic plasma with temperature anisotropy in the presence of a perpendicular AC electric field to form a hot/warm background. The dispersion relation is obtained by using the method of characteristic solutions and kinetic approach. An expression for the growth rate of a system with added cold plasma injection has been calculated. Results for representative values of parameters suited to the Earth's magnetosphere has been obtained. It is inferred that in addition to the other factors, the relativistic plasma modifies the growth rate and it also shifts the wave band significantly. The relativistic electrons by increasing the growth rate and widening the bandwidth may explain a wide frequency range of whistler emissions in the Earth's magnetosphere.
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