ABSTRACT
In the study of charged drops [1], one wants to suspend them while making observations during evaporation, and one wants to measure their mass and charge. One device for suspending them involves the imposition of an alternating-current voltage between a plate with a hole in it and two other plates equally spaced above and below the first plate. In addition there may be a constant voltage between the outside two plates to counterbalance the force of gravity Actually one might think that the constant field would be sufficient, but it allows the drop to wander providing no stable suspension point, and stray fields will cause the drop to move out of the field of observation. We shall not treat here the movement of the drop but only the calculation of the field in which the drop moves. To do this, we shall move the outside plates to infinity so that the fields become uniform at z = ± ∞. Furthermore, we shall assume that the alternating frequency is so low that the problem becomes one of electrostatics; . magnetic fields can be neglected, and the potential satisfies Laplace’s equation ∇ 2 Φ = 0 . $$ \nabla ^{2} \Phi = 0. $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108858/f4dff3a2-1feb-457b-a709-022257f02721/content/math18_1.tif"/>
