Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential

Abstract

In this work, we modeled and simulated the electric potential generated by point charges in the region of grounded conductor planes for Yukawa poten- with different values of µ . We observe that the electric potential decreases as the value of µ increases and that does not allow all the charge to be distributed on the surface of the conductor.

Point Charge between Two Grounded and Conducting Planes Forming a 60° Angle and for Yukawa’s Potential and Coulomb’s Potential

“…For the case we have discussed in this work, we can verify this if we consider 60 α =  and the position of the actual charge as ϕ =  and this result corresponds to the case of a charge between two perpendicular conducting planes. These last two cases were recently discussed [1].…”

“…It can be used Yukawa potential ( e r r µ − ) or Coulomb potential (1/r) Procedure for the calculation of the potential and electric field of a charge Q between two planes forming an angle of 60˚ > restart; > with(plots): > with(plottools): > with(linalg): > with(StringTools): > poteimgs := proc(cpoint, centerp, angplan, r, q, typec) > local charget, i, n, chargex, phi, k, epsilon, angplanx, rxy; > charget := 0; > n := abs(((360)/convert(angplan [1], units, radians, degrees))) -1; > epsilon := 8.85*10^(-12); > k := 1/(4*Pi*epsilon); > angplanx := `if`(type(r, list) or type(r, vector) or type(r, matrix), in- [2]); > rxy := `if`(type(r, list) or type(r, vector) or type(r, matrix), sqrt(r [1]…”

“…In a recent work [1], and using the Image Method (IM) [2] [3] [4] [5], we modeled and simulated the field and the electric potential produced by electrical charges in the region of grounded conducting planes using Coulomb and Yukawa potential. Our interest had its origin in the interesting works of Griffiths and Uvanovic [6], and Sallabi et al [7], who studied the load distribution in conductors using Yukawa's potential ( e r r µ − ).…”

“…In [1], we presented the expressions for the electric potential, as well as the graphs of the electric potential and the electric field for the case of a localized point charge in the region of a grounded conducting plane and for the case of two grounded conducting planes, perpendicular to each other and a point charge placed in a quadrant between the planes.…”

“…Our goal in this work is to analyze the case of a point charge between two grounded and conducting planes forming a 60˚ angle for Yukawa's potential and Coulomb's potential and to discuss the relationship between the expression of the electric potential and the cases discussed in [1]. Also, we want our work to motivate students to use computational tools in their learning of basic science subjects such as electromagnetism.…”