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