The shape of a conducting liquid droplet placed on a hydrophobic dielectric surface is simulated numerically by solving the Laplace-Young capillary equation. The electric force, acting on the conducting surface, distorts the droplet shape leading to a change in the apparent contact angle; its variation is compared with a theoretical Young-Lippman prediction. At sufficiently large values of voltage, applied to the droplet, the numerical algorithm fails to converge, which is interpreted as the break-up of the droplet surface with small droplets being ejected from the surface. These highly charged droplets, as well as any other electric charges near the triple contact line, generated for example by the electric corona discharge, cause a change of the distribution of the electric forces. This effect can be helpful in explaining saturation of the apparent contact angle: an appropriately selected surface charge near the contact line can completely stop droplet distortion, and the contact angle variation, despite the increased droplet voltage. Furthermore, the simulation results show the effect of the permittivity of the medium surrounding the droplet, on the contact angle variation.