On the electrostatic potential and electric field of a uniformly charged disk

Abstract

We calculate the electrostatic potential and electric field of a uniformly charged disk everywhere in space. This electrostatic problem was solved long ago, and its gravitational analogue was solved even earlier. However, it seems that physics students are not aware of the solution, because it is not presented in textbooks. The purpose of the present article is to fill this gap in the pedagogical literature.

Evaporation and Molecular Beam Scattering from a Flat Liquid Jet

“…Based on this picture, the evaporative flux decreases with increasing θ f , similar to how the electric field around a finite disk distorts toward the edges. 67,68 Note that the effective distance from the surface over which collisions take place is large relative to the dimensions of the liquid surface. Thus, the angular-dependent density of the vapor cloud becomes the main consideration when estimating the number of collisions.…”

“…Based on this picture, the evaporative flux decreases with increasing θ f , similar to how the electric field around a finite disk distorts towards the edges. 67,68 To lower N coll it is necessary to increase λ, which is inversely proportional to the vapor density and collision cross section σ. The vapor density is a function of liquid temperature and is limited by the freezing point.…”

Comment on ‘On the electrostatic potential and electric field of a uniformly charged disk’

“…3 Note that there is an erratum in equation (57) of [1] because the factor 1 2 was forgotten (see [2]).…”

Off-axis electric field due to cylindrical geometries of charge distribution

“…We now consider the uniform distribution of charge Q in a disk of radius R (see figure 4): as mentioned in previous section this is equivalent to the limit of flat solid cylinder. Unlike the solid cylinder and cylindrical shell the electric field due to a charged disk can be expressed in a closed form [14,15]. For uniformly charged disk, since there is no source distribution off the disk plane, the axial variable of the integrands in (2.8) can be set ¢ = z 0, so that the integrands become independent of ¢ z .…”

“…In this paper, we focus on the off-axis electric field due to uniform cylindrical distribution of charge: the formulation developed in this paper can be directly applied to the gravitational field. The off-axis gravitational or electric field due to a disk or ring has been discussed in previous articles [11][12][13][14][15][16][17][18][19][20]. In our discussion, the cylindrical distribution of charge includes four geometries, namely, solid cylinder, cylindrical shell, disk, and ring.…”