In a gas-insulated system, when the stressed conductors are encased by a solid dielectric, the corona onset voltage (COV) over its surface increases, minimizing the corona discharge. The paper's objective is to calculate the positive COV over the surface of a solid dielectric cylinder that encased rod-rod gap with a common axis and by shifting the two axes a certain distance. This calls for calculating the Laplacian electric field using the charge simulation method. The streamer inception criterion is used to calculate the positive COV at the dielectric surface for surrounding gases SF6, air, CO2, N2, argon and SF6-N2 mixture. The equivalences between the COV of SF6 and the proposed SF6-N2 mixture were performed at different pressures and dielectric thicknesses to allow confident use as an alternative insulation to SF6. The electric field and COV results agree well with the previously published values calculated by software COMSOL and those measured experimentally, respectively.