Interaction of a Straight Line Current with a Superconducting Sphere: Theoretical Results

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“…By linear superposition, the magnetic fields and the interaction forces can then be constructed for extended sources in the presence of spherical inclusions. Hence, the work reported here has provided necessary extension of the results for the superconducting sphere [2,3,10,11] that are fundamental to the advancement of MFM models and designs. Further, the our theoretical results have clearly laid necessary groundwork for modeling the tip as higher order multipoles (dipoles, quadrupoles, etc.)…”

“…Here again, the interior potential field is zero. The Neumann problem has an hydrodynamics analogue as discussed in [3,10,11].…”

“…The force on a sphere due to a circular current loop [2] and their stability [37] are determined in the Meissner state. Recently, Trombley and Palaniappan [11] determined the force acting on the superconducting sphere placed in the field of a straight line current. They found that the expression for the force can be expressed in an integral form involving a logarithmic function.…”

“…Exact results for the magnetostatic scalar potentials, interactions, levitation forces and moments on the magnets are available for a spherical superconductor [8][9][10] in the homogeneous case. A typical physical problem reduces to a Neumann boundary value problem for the Laplace equation for which closed form analytical solutions are tractable via spherical harmonic methods [2,8,9] or using analogous hydrodynamical approach [3,11]. For permanent magnets and materials with dissimilar magnetic permeability constants compared to that of the surrounding host medium the magnetic field calculations are more challenging due to 'heterogeneity'.…”

Magnetic Monopole Interaction with a Magnetic Sphere

“…Exact results for the magnetostatic scalar potentials, interactions, levitation forces and moments on the magnets are available for a spherical superconductor [8][9][10] in the homogeneous case. A typical physical problem reduces to a Neumann boundary value problem for the Laplace equation for which closed form analytical solutions are tractable via spherical harmonic methods [2,8,9] or using analogous hydrodynamical approach [3,11]. For permanent magnets and materials with dissimilar magnetic permeability constants compared to that of the surrounding host medium the magnetic field calculations are more challenging due to 'heterogeneity'.…”