With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities coincide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeΨkT is introduced. With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been been solved under a very low Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and therefore, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities coincide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeΨkT is introduced.