It is shown that the static permittivity of suspensions of charged particles in electrolyte solution can be deduced from the field-induced change of the Gibbs free energy stored outside the double layer. This energy is related to the changes of the electrolyte concentration around the particle and is obtained solving a purely static problem, The method is first verified deducing well-known results corresponding to suspensions of spherical particles, It is then used to calculate the static permittivity of suspensions of spheroidal particles, leading to a new result that cannot be analytically obtained using the classical approach.