An approximate equation for the electric potential distribution is obtained by linearizing the Poisson-Boltzmann with respect to the deviation of the electric potential from the surface potential. On the basis of the solution to this linearized Poisson-Boltzmann equation, an approximate expression is derived for the potential energy of the double layer interaction per unit area between two parallel similar plates at constant surface potential. It is found that this linearization approximation works quite well for small plate separations for all values of the surface potentials.