Dispersive electrostatic waves on the plane interface between a vacuum and a cold magnetized homogeneous electron gas are predicted for the case where an applied static magnetic field is parallel to the surface and the direction of propagation of the wave, known as Faraday configuration, and also static magnetic field is weakly non-uniform in a direction which is perpendicular to the surface. An expression for dispersion relation of these surface waves is presented based on the Wentzel–Kramers–Brillouin approximation. The dispersion relation shows the importance of the influence of the external static magnetic field gradient on the surface wave behavior.
