Volume 49, Number 6, March 2000
|Page(s)||715 - 721|
|Section||Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics|
|Published online||01 September 2002|
Current density on an arbitrary cylindrical surface producing transverse uniform interior field
Technical Physics and Prototype Engineering Division, Bhabha Atomic Research Centre
Trombay, Mumbai 400085, India
Accepted: 7 January 2000
We examine the possibility of obtaining an exact analytical expression for the surface current density on a cylinder of arbitrary cross-section necessary to produce a magnetic field which is transverse to its axis and uniform in its interior. The mathematical formulation leads to the well-studied Riemann-Hilbert problem from the theory of singular integral equations with a Cauchy-type kernel. We solve this problem for a general class of cylindrical surfaces and obtain the corresponding expression for the surface current density. As an illustration of the general class, we present a rederivation of well-known results for surface current density on elliptical and circular cylinders and also discuss two non-elliptical cylindrical surfaces.
PACS: 41.20.Gz – Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems
© EDP Sciences, 2000
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