TY - JOUR

T1 - The electric potential of an infinite conducting cylinder with an n-cusped hypocycloidal cross-section

AU - Romero-Abad, David

AU - Suárez-Córdova, Roberto

N1 - Publisher Copyright:
© 2022 European Physical Society.

PY - 2022

Y1 - 2022

N2 - Generally, during a course in electromagnetism, boundary conditions are used in conjunction with the Laplace equation to determine the electric potential of a system of objects in regions of space free of electric charges. However, for objects with unconventional geometries such as the hypocycloid, this is not an easy task. In the case where the problem can be reduced to two dimensions, there are simpler approximations such as complex-variable with conformal transformation. In this work, we use the last approach, to calculate analytically the electric potential of an infinite conducting cylinder with an n-cusped hypocycloidal cross-section and charge Q per unit length. In addition, we verify some of the results using numerical methods. The target readers of the paper are students pursuing physics at the introductory undergraduate level.

AB - Generally, during a course in electromagnetism, boundary conditions are used in conjunction with the Laplace equation to determine the electric potential of a system of objects in regions of space free of electric charges. However, for objects with unconventional geometries such as the hypocycloid, this is not an easy task. In the case where the problem can be reduced to two dimensions, there are simpler approximations such as complex-variable with conformal transformation. In this work, we use the last approach, to calculate analytically the electric potential of an infinite conducting cylinder with an n-cusped hypocycloidal cross-section and charge Q per unit length. In addition, we verify some of the results using numerical methods. The target readers of the paper are students pursuing physics at the introductory undergraduate level.

KW - complex variable potential

KW - conformal-mapping

KW - hypocycloid

UR - http://www.scopus.com/inward/record.url?scp=85128978572&partnerID=8YFLogxK

U2 - 10.1088/1361-6404/ac5e7e

DO - 10.1088/1361-6404/ac5e7e

M3 - Artículo

AN - SCOPUS:85128978572

SN - 0143-0807

VL - 43

JO - European Journal of Physics

JF - European Journal of Physics

IS - 3

M1 - 035205

ER -