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Two dimensional transverse Kelvin-Helmholtz (K-H) instability has been studied at the interface between the two fluids (plasma medium) of finite thickness in relative motion to each other. The perturbations on the interface are assumed to be electromagnetic and a dispersion relation is obtained. The interface (boundary) has been found to be unstable for a wide range of perturbation wavelengths (wave numbers kx, ky). It is shown that the modification introduced by electromagnetic (quasi-electrostatic) perturbations in comparison to electrostatic one is to reduce the growth rate of perturbations. The growth rate maximizes when kx = ky. The applications of this study have been discussed to explain some of the observed ionospheric (auroral arc formation) and magnetospheric (unstable magnetopause boundary, hydromagnetic pulsations) phenomena.