New solution method for the problem of a uniformly charged straight wire

Abstract

A common problem in electrostatics is determining the electrostatic potential due to a uniformly charged straight wire. The solution of this problem illustrates well the types of calculations that one must perform in order to obtain the electrostatic potential or field of a given continuous charge distribution. In this work, we reconsider and solve the problem of a uniformly charged straight wire via a new method that is different from the popular direct integration approach found in the majority of physics textbooks. The outcomes of the two methods are compared and the results suggest several interesting mathematical formulas involving special functions.

Forcing Twisted 1,7‐Dibromoperylene Diimides to Flatten in the Solid State: What a Difference an Atom Makes

“…Worthy of note, the occurrence of infinite stacks of homochiral (twisted) molecules, where the offset of the Br atoms generates a weak dipole (0.35 D in 0 Br ) may further stabilize, through an infinite number of dipolar interactions, the twisted conformer. However, using Ciftja's model [24] and the stacking parameters shown in Figure 3, such stabilization falls near 0.1 kJ mol −1 , that is two orders of magnitude lower than π–π stacking, and is, in our discussion, a negligible term.…”

Correspondence between Electrostatics and Contact Mechanics with Further Results in Equilibrium Charge Distributions

“… Uniformly charged rectangular plate. The exact calculation of $$U(L_x,L_y)$$ is very challenging with the final result obtained by Ciftja [ 73 ] that reads: $$$$\begin{eqnarray} U(L_x,L_y) &=& k_e \, Q^2 \left(\frac{1}{L_x} \, \sinh ^{-1} {\left(\frac{L_x}{L_y}\right)} +\frac{1}{L_y} \, \sinh ^{-1} {\left(\frac{L_y}{L_x} \right)}\right. \nonumber\\ &&+\left.\frac{1}{3}\left[\frac{L_x}{L_y^2} +\frac{L_y}{L_x^2} - \left(\frac{1}{L_x^2} +\frac{1}{L_y^2}\right)\sqrt{L_x^2+L_y^2}\right]\right) \end{eqnarray}$$$$ Uniformly charged equilateral triangle.…”

Electrostatic potential of a uniformly charged annulus

“…Prominent examples that feature in almost all calculus-based undergraduate physics textbooks that deal with the topics of electricity and magnetism [1][2][3][4][5][6][7] are objects like a uniformly charged finite line, ring, disk, spherical surface and solid sphere. The 1D case of a finite line with constant linear charge density is easy to handle by direct integration using a variety of methods [8]. The 3D case studies of a conducting spherical surface with constant surface charge density and a non-conducting solid sphere with constant volume charge density are perfect examples that illustrate the application of Gauss's law to derive the electric field.…”