The Lippmann-Young equation has been widely used in electrowetting to predict the contact-angle change of a droplet on a insulating substrate with respect to the externally-applied electrical voltage. The Lippmann-Young equation is derived by assuming a droplet as a perfect conductor, so that the effect of the electrical double layer and the line tension are not taken into account. The validity of the assumption has never been checked before, systematically. In the present investigation, a modified Lippmann-Young equation is derived taking into account of the effect of the electrical double layer and the line tension. To assess their influence on contact-angle change in electrowetting, the electrostatic field around the three-phase contact line is analyzed by solving the Poisson-Boltzmann equation numerically. The validity of the numerical methods is verified by using the past theoretical results on the electrostatic field around a wedge-shaped geometry, which shows fairly good agreement. The results of the present investigation clearly indicate that the effect of the electrical double layer and the line tension is negligible for a millimeter-sized droplet. On the other hand, for a micron-sized droplet, the effect of the line tension can become a dominating factor which controls the contact-angle change in electrowetting.