Related papers: Electrostatic potential of a homogeneously charged…
We calculate the electrostatic potential of a periodic lattice of arbitrary extended charges by using the Cartesian multipole formalism. This method allows the separation of the long-range potential from the contact potential (potential on…
Dimensional analysis, superposition principle, and continuity of electric potential are used to study electric potential of a uniformly charged square sheet at its plane. It is shown that knowing the electric potential on the diagonal and…
We study the problem of finding a point of maximal electrostatic potential inside an arbitrary triangle with homogeneous surface charge distribution. In this article we derive several synthetic and analytic relations for its location in the…
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 - even earlier. However, it seems that physics…
We evaluate the electrostatic potential and the electrostatic field created by a point charge and an arbitrarly oriented electrical dipole placed near a grounded perfectly conducting sphere. Induced surface charge distributions as well as…
In the study of colloidal, biological and electrochemical systems, it is customary to treat surfaces, macromolecules and electrodes as homogeneously charged. This simplified approach is proven successful in most cases, but fails to describe…
The starting point is the problem of finding the interaction energy of two coinciding homogeneous cubic charge distributions. The brute force method of subdividing the cube into $N^3$ sub-cubes and doing the sums results in slow convergence…
The general form of the electrostatic potential around an arbitrarily charged colloid at an interface between a dielectric and a screening phase (such as air and water, respectively) is analyzed in terms of a multipole expansion. The…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole…
All existing derivations of the electrostatic potential of a uniformly charged disk are technically rather involved. In an old and now almost forgotten publication, Duffin and McWhirter proposed a method for calculating the electrostatic…
Gravitational potential and gravitational energy are presented in analytical form for homogeneous rectangular parallelepiped.
A multiple-image method is developed to accurately calculate the electrostatic interaction between neutral dielectric particles and a uniformly charged dielectric substrate. The difference in dielectric constants between the particle and…
For several configurations of charges in the presence of conductors, the method of images permits us to obtain some observables associated with such a configuration by replacing the conductors with some image charges. However, simple…
The non-relativistic static and dynamic dipole polarizabilities of hydrogen atom experiencing a cylindrical confinement are investigated. Two methods based on B-Splines are used for the computations of the energies and wavefunctions. The…
Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient…
We examine the spatial distribution of electric charges within an extended, non-conductive cylinder featuring an inner radius denoted as $r_{0}$. Our investigation unveils the emergence of a distinct modified attractive-inverse square…
Two dimensional electric potential maps based on voltage detection in conducting paper are common practice in many physics courses in college. Most frequently, students work on `capacitor-like' geometries with current flowing between two…
For a theory with a pseudo scalar coupling $\phi F\tilde F$ and in the case that there is a constant electric or magnetic strength expectation value, we compute the interaction potential within the structure of the gauge-invariant but…
The concept of complex harmonic potential in a doubly connected condenser (capacitor) is introduced as an analogue of the real-valued potential of an electrostatic vector field. In this analogy the full differential of a complex potential…