The dispersion relation for the whistler mode waves in an isothermal one-component electron plasma in the presence of a parallel electric field has been derived from the linearized coupled Boltzmann-Maxwell-Vlasov equation. The presence of a parallel electric field introduces a change in the zero-order distribution function through the modification of electron thermal velocity in the direction. As a result of this asymmetric energy transfer, the distribution function becomes temperature dependent and complex. By using this feature, expressions for the growth rate instability have been derived. These results have been used to study the growth rate of whistler mode waves propagating in the magnetosphere. Their growth has been computed by using the observed plasma parameters at 6.6RE. The variation of growth rate along a given geomagnetic field line has also been computed, and the growth rate is found to be maximum in the equatorial magnetosphere. In the absence f the electrostatic field the growth rate relaxes to zero, which clearly indicates that in the case of isothermal magnetoplasma the growth rate is induced by the electrostatic field.