The electrospray ion source has recently revolutionized mass spectrometry by allowing researchers to produce gaseous ions of very large molecular weights such as proteins and polymers. The process by which these high-molecular-weight ions are produced, however, is not very well understood. The purpose of the present work is to study the fields in the vicinity of each charge in order to shed some light on the ion formation process for charged dielectric droplets. An important feature of this work, therefore, is the treatment of the charge as discrete rather than continuous. The picture that emerges is of discrete charges in a dielectric droplet thermally oscillating around a potential well, located slightly below the droplet surface. The charges produce localized electrostatic pressures on the droplet surface that are higher (15.5 and 70% for dielectric constants of 80 and 20, respectively) than expected if the charge distribution were continuous. These high localized pressures could locally stretch the surface and result in the emission of ions or small charged droplets. The magnitude of these localized pressures is a function of the number of charges and the dielectric constant of the droplet.