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 -